If you are using .Net, I'd recommend checking out NUnit. It's a great testing framework to use.
As far as learning about the "testing method", there are many different ways to test an application. When using a tool like NUnit, for example, you are writing automated tests which run without user interaction. In these types of tests, you typically write tests for each of the public methods in your application, and you ensure that given known inputs, these methods produce the expected outputs. Over time as the application changes (via enhancements, bug fixes, etc.) you have a core set of tests that you can re-run to ensure nothing breaks as a result of the changes. You can also do failure testing to ensure that given an invalid set of inputs to a method, it throws the proper exceptions, etc.
Besides automated testing with a tool like NUnit, it's also important to ensure that your end users test the product. "End users" here could be a Quality Assurance group in your company, or it could be the actual customer. The point is that you need to ensure that someone actually uses your application to make sure it works as expected, because no matter how good the automated tests are, there will still be many things you won't think of that your users will discover. One way to approach this type of testing is to write test scenarios, and have your users execute them to make sure the scenario results in the correct behavior.
I think the best testing approach combines both of the above, namely automated testing and user testing (with documented test scenarios).