There are two ways to do it, one is with NSApplication and the other is with NSWindow.

To do it with NSApplication, you’ll make this simple call

   [[NSApplication sharedApplication]
           setPresentationOptions:NSFullScreenWindowMask];

To do it with NSWindow you’ll make this one

   [window setCollectionBehavior:
             NSWindowCollectionBehaviorFullScreenPrimary];

There is also an NSWindowCollectionBehaviorFullScreenAuxiliary that you can use to allow auxiliary windows to show up in the space with the main window.

Calling either of these methods will add the resize button to the upper right corner of the window. You can call them at any time also. If you want it to be in the app all the time, call it somewhere like applicationDidFinishLaunching.

One thing to remember is that fullscreen functionality like this is LION ONLY. If you’re using this in an app that targets more than 10.7, make sure to do the appropriate checks around this code.