How do you get the dome light cover off in a 2001 Grand Prix GT?

You should be able to pop it off by inserting a small screwdriver along side the plastic lens and just pop it off, or a thin pocket knife

Try using a screwdriver to release the 2 clips in the front holding the unit (Not just the lenses) into the holder that's attached to the headliner. It's a 2 piece unit.