Patching techniques vary depending upon the size of the hole. For a golf ball sized hole, the “Pumpkin Patch” works quite well.
With a key holesaw, cut away the damaged area in any shape you desire, but angle the blade like the top of a pumpkin cutout. Next, cut a scrap of sheetrock as closely as possible to the same shape and size of your damaged cut-away spot. With a razor knife, bevel the edges to match the angle of the hole. You can fine-tune the fit by holding the piece over the hole and running the holesaw along the two edges together until it fits flush. Then, using 15 or 20 minute mud, butter the edges of the new piece and around the edge of the hole in the wall. Push the piece into place and smooth over with a drywall knife. Use a hairdryer to speed up the drying process. When set, skim another layer of regular mud or 15-minute mud (depending upon the time you have to allow it to set) on the spot you are trying to patch. Dry, sand and then you are done. If texture is needed, a spray can works well. Practice on some paper first.
For larger holes we often will use a “screw backer board” like the photo above. Simply cut rectangle larger than the hole and install. Then follow the "Pumpkin Patch" steps described above.