I would like to copy my android project and create a new project form the same files just with a different name. The purpose of this is so I can have a second version of my app which is ad supported in the app store.
I found this answer here:
Android - copy existing project with a new name
But its for eclipse, how can I do this in Android Studio?
The steps in the link you specified should also work for Android Studio. Just make a copy (using a file manager) of the entire module folder and give it a new name. Now open it up and use
Refactor -> Rename (right click on the item you want to rename) to rename your module and package.
See this for details about refactoring in IntelliJ/Android Studio.