what I use and like. Many patching methods vary when the stud is in the hole. This will make things easier because you now have ONE nailing board to use.
So, here are two scenerios. The hole is between two studs so you have nothing to nail to.
First cut the hole in the wall out to make a perfect square. Round the length and width sides to the nearest whole figure measurement. Use a drywall saw, its a manual saw like an icepick in size. Now, lets say the hole is 6 x 4. Now, get a repair piece of drywall the same width and cut a 6 x 4 square for the plug. OK, now you have a hole and a plug, but as you see nothing to nail to it. Now, cut a 1 x 4 piece of wood that is 8 inches long, cut two pieces. Now on each end of the hole run that piece into the hole and up and down from the 4 inch side of the hole. Hold it in place and with a screw driver, screw through the rock into the upper end of the wood and tighten it as so the head will slightly counter sink into the rock. Now do the bottom of that board and then the same with the other board. when done you will have two boards visible and for something to nail to.
Now insert the plug and now screw this plug into the boards, you will know where they are by the screws in the wall. Counter sink the heads slightly. Now with joing compound trowel around the joints and the screw heads. let dry for 24 hours, then sand and add more if necessary as this stuff shrinks.
Now if the hold goes from one stud to the other. cut the hole out square again and cut your patch. Now you sister a board alongside each stud so you have a nailing board alongside each stud. You will screw the patch into this sistered board. do the same patching filling as above.
This should do that.
Its really very easy, you just have to make soemthing inside the hole a nailing board to fasten the patch to.