How to run windows form application on other system

You can't necessarily just compile a program and copy the EXE file to a different computer - and C# program needs the whole of the .NET framework as a minimum, and the correct version of the framework as well (some are included with Windows, but not the most recent ones.
In addition your code may require access to DLL files which need to be included or installed in the right place, and (depending on how you write the app) connection strings and / or configuration files may need to be changed.

We can't do any of that for you, but creating an installation program is a good start, but if your app stops after a few seconds, then you need to start thinking about why - and it's likely to be connection string / config file related.

Start by adding logging to your app to find out how far it gets and where it dies: a basic text file that you append lines to at different points in your app is a simple starter (I'd suggest using File.AppendText). You then review the file after the app closes When you know the rough area that it fails in you can "focus" your logging information to narrow down how far it gets. When you have a good idea which code it's failing in, you can start looking at why, but not before.