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how to publish a windows form app with its database in C#

I make a windows form application with its database and I want to publish it . the app is running in my system so good but when I run it in another PC its shows errors about cannot connect to its database.
also I put database mdf and ldf file in program folder but my app doesn't work.
and this is my connection string :
string connectionSt = "Data Source=DESKTOP-NLKJ55F;Initial Catalog=IndustryContracts;Integrated Security=True";

This is a common mistake for people learning how to develop apps with databases.
Basically: You have the wrong approach. A database is not really meant to be created at every computer where a program is installed. Rather, the ideal use case for a database is one which is created in a server, and any app that requires to use it will simply connect to it, by some protocol like TCP. This helps with encapsulation and also makes your application more compact.
So normally when the program needs to read and write data to be saved somewhere, people usually go with methods such as writing into a CSV file, or a tab delimited file, and then reading from those files.
There is also another option, which is to use a serverless DB such as SQLite, however, this would mean you need to learn how to implement said database.
Lastly, as a really discouraged way to do it, and a bit of a "brute force" approach, you can copy the database creation script, install a DBMS in your target computer, run the script to create the DB, then change the connection string of the DB in your program to match the newly created instance, then install the program. See how extremely clunky that was?
Remember: Most databases run in a server, even if that server is your PC, hence why they're referred to as instances. Naturally a server shouldn't be replicated every time a program is installed.

Deploying entity framework code first with production database

I've developed a pretty simple web app using entity framework code first. I realized after hours of frustration that even though localdb is SQL Server Express it is actually not meant to be used with production when using 'publish' (the publish wizard). FYI I'm using EF 6.1.3, SQL Server 2014, VS 2013, and IIS 7.
If I understand correctly, when you click publish with localdb, all you're really doing is copying your localdb database to your IIS 7 server. I couldn't figure out why that when I updated my lodaldb database through VS migrations that my production server database wasn't being updated. I understand (and believe now) that it's actually two different instances of localdb, and hence not the same data.
OK whatever - I'm done with localdb and I created a real SQL Server 2014 db on my machine. I've googled for hours and can't figure out what to do now. I have some questions:
How do I manage this new database using EF? For instance, suppose I want to add a new column. First I add it to my localdb, do some testing, and do the migration using Add-Migration blah then Update-Database... Do I then have to generate a SQL script using VS and then manually run that on the production DB server?
I know this isn't great, but instead of using local DB with entity framework, can I just attach EF to a real staging SQL Server database (a test one) and skip all this localdb bull****? Then could I manage it using code-first migrations and keep everything in sync?
Am I supposed to use an Initializer? I've read conflicting reports about whether to use these or not for a production db (like this one)
public class PricedNotesInitializer: MigrateDatabaseToLatestVersion<...,...> {
}
It's frustrating that the only way I learn about this stuff is through blog posts from other people frustrated. I don't understand why the documentation is so garbage.
Thanks for your help and sorry for the rant.

Using an initializer
You can use the MigrateDatabaseToLatestVersion initializer so schema changes to the database will be (if possible without data loss) done automatically when your application first starts up after a deploy.
If data loss would occur you'll get an error and have to take appropriate action. This can be overriden to proceed even with data loss.
Development environment setup experience
As other answers already pointed out, you need one connection string per environment so the LocalDB is fine for development, I would even encourage it because it can be created and initialized (and seeded with test data) automatically for any new developer that needs to develop or debug it just by building and running the application from source.
The "set up new development environment" experience should be as smooth as possible with as few and preferably zero manual steps apart from loading the solution, building and running the code-base.
Automate your release cycle
Your deploy and release pipeline should be automatic and not require any manual commands that might be executed wrongly, be forgotten or worse.
What could be a manual step is a simple yes/no approval on the staged changes if you want to be careful or fulfill some compliance requirements.
Automated tests in your staging environment should however alleviate this and when successful automatically deploy to production - in a perfect world ;)
Running update-database manually against production requires that whatever machine is running it has access to the production database - an unlikely or not-recommended scenario if you're running it interactively I would say. If required you could script it as part of your automated deploy pipeline if you want more control over it than using the initializer, which seems best suited for simpler projects (which this one seemed to be though).

Thanks everyone for the help. I figured it out using your guys' help. For anyone interested in the steps, here they are. I'm just going to list some extra help here but the above answers truly answer the question. This assumes the set-up in my question. Once you have your database set-up, I would recommend you update it with your local db like so:
In VS2013, go to Tools -> sql server object explorer -> (LocalDb)\v11.0 -> databases -> [database_name] -> right click -> Data Comparison -> schema compare
In the right drop down, find your SQL database and test the connection to make sure it works.
Click compare -> Update Target (I wouldn't recommend this for production databases but if it's a staging db you just created, it's fine)
If you go SSMS (SQL Server Management Studio), you should see the new tables and whatever the schema compare tool made. Great!
If you want to use an initializer, go ahead, just make sure it's set to CreateDatabaseIfNotExists or something that won't drop the database. I mean I guess you could use anything you want, but it would defeat the purpose of the above steps.
Right click your web project, click publish, use web deploy, go to your databases, target your new database, ensure Execute Code First Migrations is checked (this will run all the migrations you've done for your localdb on your new database). You don't actually have to do this. You can alternatively leave this unchecked and do what Sampath recommends in the accepted answer.
Done! Now you've successfully converted to a real SQL Server Express DB.
To manage your database, just follow the answers above. Alternatively, use the publish wizard again, ensure Execute Code First Migrations is checked and publish!

You should have two connection strings, one for your localdb and one for your production SQL server.
You should develop as normal, for example using add-migration and update-database for your localdb.
Then when you are ready to publish to live should you change your connection string to your live one. Publish your site. Then run the update-database command. This will sync your live database to what you just published.

If you work on SQL express edition locally then you can migrate it pretty easily to the SQL production server.SQL production server can be a SQL Azure or your own production server.
A 1. You just need to change your local connection string to a production one and run below command on package manager. Then all your not updated migration scripts will run on the production.
PM> Update-Database
A 2 : I don't recommend this method.
A 3 : You can do that like this :
Database.SetInitializer(new CreateDatabaseIfNotExists<YourDbContext>());

Can't see my Northwind DB when adding connection in Visual Studio

As a beginner in C#/VS I want to practice making basic LINQ queries on simple DB's. I downloaded the "famous" Northwind and Pubs databases on the official Microsoft websites (https://www.microsoft.com/en-us/download/details.aspx?id=23654). It gave me a .msi files that installed 6 files on my c: instnwnd.sql, instpubs.sql, NORTHWND.LDF, NORTHWND.MDF, PUBS.MDF, PUBS_LOG.LDF.
When I launch Visual Community 2015 and simply make an "Open => File..." and open the "instnwnd.sql", it opens the .sql file without problem. The problem is when I'm trying to make a connection to the database, being either through the Solution Explorer (Data Connections => Add Connection) or while I'm trying to create an EDM (Database first), which is what I want to do eventually.
The exact problem is that one : the Northwind and Pubs databases doesn't show up in the database list when i'm trying to add a connection, I only get the system databases. Here is what I get :
http://img15.hostingpics.net/pics/128870screenshot1.jpg
I read many MSDN documentation pages and several StackOverFlow topic about the matter (the closest of solving my issue was that one, but didn't work :How to connect to LocalDB in Visual Studio Server Explorer?). I have SQL Server Express 2014 with tools, started SQL services in my Windows Services etc.
What should I do in order to have those databases available so I can generate code and starting making my LINQ exercices ?
Thanks in advance !

You need to attach the databases before you can see them**. You're having a problem attaching the databases due to versioning (which is odd), but your sample db's are very old. Perhaps try newer ones from here https://northwinddatabase.codeplex.com/ and make sure you attach them before expecting them to show up in the tools.
** Technically this is not true. I believe there is a way of connecting to sql server and passing a file path in the connection string, however this will likely still fail for your due to the error you get trying to attach the dbs you have. Additionally, it requires a specially crafted connection string which may or may not be usable with the gui tools you're trying to use. It is also, in my opinion, a less common way of accessing sql server databases, so I would stick with attaching them first. If you want to find out more about this, I believe the feature you need to research is called 'sql server user instances'.

Database corruption

I am planning to use localdb for next project and thinking of making rotating backup of database (it will be detached normally and only attached when software is running). And I was thinking how to do automatic restore from backup. This required me to know if database is corrupted. And I can't find anything about this subject.
My guess, peoples don't care on that level about database integrity. Backup and maintenance is a job for IT, there are dozens of tools for SQL Express.
My database will be local on PC and not big. I want to make it very simple:
detect if database is corrupt (how?)
offer user an option to restore database from most recent backup (this is easy)
P.S.: perhaps I don't know something about sql express, localdb, linq-to-sql. This is why question is very generic.
After getting answer I'll go with simple options:
if database can't be opened and file exists - database is corrupted, offer restore (not exists - create empty database and do initial setup);
provide following options (if user noticed something unusual or get errors during update, etc.): to check database DBCC CHECKDB (0, REPAIR_REBUILD) (could be good to try first) or to restore.
Automatic detection seems costly. Rather keep weekly/montly backup for manual restoration (if that would be really necessary for old data) and create mdf-file backup every run to minimize loss to 1 day maximum (which in my case is totally fine for an abnormal situation like database corruption).

I am planning to use localdb for next project a
You mean you plan to run a database that is explicitly not made for running in production on production?
And I was thinking how to do automatic restore from backup. This required me to know if
database is corrupted. And I can't find anything about this subject.
Read SQL documentation. Backusp, restores are all doe using standard SQL Commands. Totally easy to do that.
I want to make it very simple:
detect if database is corrupt (how?)
DBC Checkdb command. Can take a lot of time, though, depending on the database.
perhaps I don't know something about sql express, localdb, linq-to-sql.
This can be solved by reading the documentation. I would for example never use localdb on anything production.
Read the documentation? It starts with the first line:
Microsoft SQL Server 2014 Express LocalDB is an execution mode of SQL Server Express
targeted to program developers.

Database Deployment Practices

I have deployed plenty of software to my clients. Mostly are Window Forms applications.
Here is my current practice.
Manually install SQLExpress and SQL Management Studio to each client PC.
Then use ClickOne to install the code from the server.
When there is a changes in code, I will use ClickOne to deploy -(NO PROBLEM with this step)
But when there is a change in a database column, what do I do?
I have even tried writing a database update script. Each time the program starts, it will read through the .sql update file and run them if the database exists. This solves the problem of updating the database columns, but it does not help in my DEBUGGING work when my customer complain there is a wrong data. At that point, I have to personally go to their site to check it out.
I find it difficult to have the database installed on the client PC as it make my debugging work very very difficult. I am thinking about moving my client database to a host on an Online server. But that then comes with these constraints:
What if the internet is down?
What if my customer has no internet?
Could you help to advise me? Is this a common problem faced by developer? What is the common practice out there? Does Window Azure or SQL CE help?

Depending on the data I would recommend using SQL CE.
If the data isn't too much, speed is not the primary goal (CE is slower than Express) and you don't need DB-Features not supported by CE (e.g. stored procedures) it is the better choice IMHO, because:
The client does not need to install a full SQL server (easier installation/deployment)
You do not have problems with multiple SQLExpress instances
Your SW doesn't need to worry if there even is a SQL instance
Less resources used on the client side
Additionally the clients could send you their SQL CE DB-File for inspection and you do not need to go to their site.
It is also relativly easy to implement an off site sync with SQL CE and MS Sync FW.

Installing one database per client PC can be tricky. I think you have a decent handle on how to deal with the issue currently. It seems like the real issue you are currently facing is debugging. To deal with this, there are a couple ways you could go:
Have the customer upload their copy of the database back to you. This would provide you with the data they have and you could use it with a debug copy of your code to identify the issues. The downside is that if the database is large it might be an issue transferring it.
Remote onto the customer's machine. Observe the system remotely using something like CoPilot. That way you could see what is happening in its natural environment.
There are probably other ways, but these are a couple of good ones. As for using an online database, this is an option but it brings its own set of issues with it. You mentioned a couple. As for Azure, that is cloud-based (online) so the same issues will apply. SQL CE won't help you any more than your current installation does.
Bottom line is that I would recommend you look into the ways to fix your one issue (as listed above) instead of creating a whole new set of issues by moving to an Internet-based solution. I would only recommend moving to the Internet if it was addressing a larger business need (for example, mobility). Doing the same thing you have been doing only online will probably just make life harder.
To recap the comments below since they are so pertinent to the issue, if you are choosing between file-based databases that don't need to be physically installed on the machine, your best choices are probably between SQLite and SQL CE. Microsoft supports SQL CE better but it is a larger package and has less features than the trim SQLite. Here is a good discussion on the differences:
https://stackoverflow.com/questions/2278104/sql-ce-sqlite-what-are-the-differences-between-them
However, the issue gets more complicated when you start looking at linq2sql since that is designed for SQL server. Microsoft does not support SQL CE with linq2sql out of the box, although there is a work-around that will get it to work:
http://pietschsoft.com/post/2009/01/Using-LINQ-to-SQL-with-SQL-Server-Compact-Edition.aspx
SQLite is not supported at all with linq2sql but there is a way to use linq to talk with SQLite:
LINQ with SQLite (linqtosql)
This library also supports other common databases including MySQL and Firebird.

You could use the SQLCMD utility to execute the change script, as mentioned in this related question