I want to check when the user double click on applictaion icon that no another instance of this application is already running.
I read about My.Application but i still don't know what to do.
The most common pattern for doing this is to use the Singleton pattern. As you haven't indicated a language, I'm going to assume that you are referring to C# here - if not, the principles are still the same in most OO languages.
This article should give you some help.