Probably best to go through the tutorials included in the maya help files at some point, but I'll write something up quickly here.

Start with your box and your lid with the lid flat on top of the box (closed). The edge of the box and the edge of the lid should be touching.

Now you need the lid to rotate properly. Select your lid, and hit 'w' for the move tool. The manipulator (axis arrows) will likely be right in the middle of the lid. Hit 'home' (on mac) and the arrowheads will disappear allowing you to move your pivot point. Move the manipulator to the edge of the lid just where the box and lid are touching. Hit 'home' again to exit.

Test your rotation. Hit 'e' and rotate the lid in whichever axis, allowing the lid to open and close. All that's needed now is to key it.

Start by keying the lid closed at frame 1. Hit Shift - E with the lid closed. A red tick will appear at frame 1 and your rotate channels will be colored indicating they are keyed.

Move to frame 10 or whenever you want the lid to start opening. Hit Shift-E again to key, (alternately, select the correct rotate channel, right click on it and hit 'Key selected')

Move to frame 15 or whenever you want the lid to be fully open. Rotate the lid to the open position and hit Shift-E again to key it as open. Great!

Scrub in the timeline (LMB back and forth) to see the result, or hit play.