You can use a Rotozip tool. This is what professional drywall installers use. See the link below to buy one through Amazon.
You can pull the corner screws out from the box, place the sheet of drywall on it and make sure it is in the correct place and then hit the drywall with your hand and the marks will show up o the backside. Draw the box in and then use a pointed drywall saw to cut out the piece.
Draw your box on the drywall at the position you want it to fit. Drill a hole inside of each corner. Cut between the holes on the lines of your drawing with a mat knife "box cutter". Cut down but not through all four lines; then push down and this will break the dry wall at the cut. If it is too rough or not quite big enough an opening, just use a heavy grit sand paper to sand back to the size you need.
Hi Jan! During a recent repair at my house, I watched a professional do it, and it was impressive because he measured side to side and top to bottom and bottom to top. He got it perfect the first time. I do that, too, but, have also used chalk to outline the box lined up the piece of drywall and pressed it against the electrical outlet. Then I cut out the outline.