Go to Home Depot and buy another piece of drywall, some compound, some compound tape, a spreader thingy, some sandpaper made for compound sanding...and your set.
Cut out the broken part, in a square. Cut a new piece exactly to fit. Set the piece in there. Use some drywall screws to hold it in place. Put tape where the edges meet each other. Then, take compound and spread it on there with the spreader, get in in the cracks nice and good. Let it dry, sand it off some, then apply more. Do it again if you see nessesairy. Apply some paint, and your done
. Im 16 and I can do it.