<<< make sure that the hole is square and it goes from stud to stud. If the square is perfectly drawn and measured, this sure makes the patch job easy. >>
Clarification: From center of stud to center of stud. Then use drywall screws to hold the piece in place. Make sure you tape the seams or they will never hold.
I would not suggest painting over the old drywall that has had it's paper sheeting comprimised - I tried that and it didn't work very well. Not to mention the slight indentations from where the paper was ripped is very visible, even with perltex in the paint.