Mike asked for help in repairing a large hole in drywall, so we built a model with several alternatives. All of them work. Follow this link to the Learning Curve Tab for a video on all of this.
The traditional technique is to slide wood, or even drywall strips into the wall and screw them into place, permitting you to place a piece of drywall over them and screw it down flush with the wall. Then of course you have to tape and plaster the crack all around.
Another viewer suggested using window screen and spray on adhesive. Then you can simply use regular drywall compound. You can see how it flows slightly through the screen to get a really good hold. Manufacturers now make large patches like this with the stickum already on the back side. They even make perforated metal plates to give you strength on this job. With this technique the joint has tape over it as part of the patch.
One renovation contractor technique is to simply cut the hole square, then cut a piece of drywall about 4 inches larger than the hole. Score the back side of this patch and peel off the drywall, leaving you with a piece that will fit into the hole, with it's own built in flange. Compound under and over the flange and you have a good patch as well.
Probably the strongest and quickest of the patches is to use drywall frogs. We call them frogs because they appear to have two little legs that stick out in the front. These sturdy pieces of metal mesh clip right onto the edge of the hole. Drive a screw through and it easily penetrates and grabs the frog, making a solid support behind the drywall. Place in your patch of drywall and screw it into place. Then bend off those frog legs, they break off below the surface of the drywall. Nothing is in the front but you have great strength bridging the joint between the wall and the patch. These are very useful to prevent sagging when you butt two pieces of drywall together on the ceiling. They are starting to become commonly available in the renovation stores.