You don't need to sister an entire 2x4 to the stud, just a 2x2 will do. I prefer to use screws instead of nails. I drill a pilot hole in the 2x2 at a slight angle, then holding the 2x2 in position, I set the screws in. This method keeps the 2x2 flush with the stud. I've tried cutting the drywall down the center of the stud, but it's too time consuming and you have to put the drywall screws or nails at an angel and try not to break the edge. Having 1-1/2" to screw/nail to it much easier. I use a 2x2 that is slightly longer than the patch so I have an end under the old drywall on both sides of the patch. I just did one of these yesterday, and it was so simple.