I never use unitests in my apps . I know that exists many technologies for testing .NET based application. (For example NUnit). Which of this tools more comfortable and more understandable to use. Please can you show the good articles where can I find information about unitests and understand key situation where I must use them?
NUnit is pretty good, and it integrates well with Visual Studio. If you're just starting, and have no uncommon requirements, there is no reason to choose a different tool.
NUnit has a QuickStart guide that you could follow. It notes that it "isn't a good example of Test-Driven Development": it starts with some code, then adds unit tests, whereas TDD does it the other way round. But TDD practices aside, the QuickStart is still a good introduction to NUnit.
I always use MSTest, which is included in the professional edition of Visual Studio 2008 and up. It doesn't have the broad feature set as other unit testing frameworks, but it serves me well.
When you want to learn how to write good unit tests, you should definitely read Roy Osherove's The Art of Unit Testing. The book explains it very well and nice plus is that the book is pretty thin. So it wouldn't take you that long to finish it.