[drcoastline]

The best way (and the right way) is to cut the dry wall to fit properly. If you are not going to do that. Cut pieces to fit the gap apply construction adhesive and push it in place. Spackle and tape over the seam.

You can dry joint compound quick with a heat gun or hair dryer. For an entire room crank up the heat and put a fan in the room or a space heater.