It's actually really simple. There's actually two different modes, but they're accomplished the same way. One is that menu is off screen and slides in to overlap the normal view. The second is the the view is in the background, and the normal view slides off to reveal the menu.

In both cases, you simply have a front view and a rear view. All you need to do is adjust the frame (positioning) of one of the views and animate that transition. Animating view transitions is really easy in iOS. So the pseudo code for this basically becomes:

Menu.position.x = Menu.position.x + (.7*screensize);

Animate();