When patching a large hole in drywall you can simply put some plaster on a board or a piece of drywall, slide it into the hole and then pull it back tight against the backside of the hole. After the plaster has set, you can then plaster the drywall patch into this bar across the hole.
You can also use things called "frogs", metal clips that have a lot of holes in them to receive drywall screws. The clip onto the edge so they will hold themselves into place long enough for you to place the patch and put drywall screws through the good wall and through the patch into the frog. Then the clips that are sticking out the front side are simply broken off below the surface. In the photo the left clip is broken off.