You can run applications right from IntelliJ IDEA. All you need is to have an SDK set up for your project/module.
If you are not going to pass any parameters to your program, and your program does not require any specific actions to be performed before start, you can run it right from the editor.
Click the Run button in the gutter near the class declaration and select Run.
If you are going to pass any parameters to your program, add any VM options (for example, to allow remote debugging), or otherwise customize the startup of your program, use a run/debug configuration.
On the main toolbar, select the run/debug configuration you are going to use.
Click Run or press Shift+F10.