OK, what I did when a towel holder was accidentally pulled off a wall taking a 2 x 3" piece of plasterboard with it:
I trimmed the hole neatly (ie bits of torn paper and loose plaster off- use a stanley knife and be a bit brutal- you need a clean edge)
I got a small piece of thin ply wood or similar (not cardboard which absorbs too much water or glue and might buckle!).
I drilled a 2 small holes in the centre of this and threaded a piece of string through so they came out the same side.
I cut the ply sheet to a size that I could slip in through the hole but was wide enough in at least one dimension so it would sit against the back of the holed plasterboard. You need this piece to be as big as possible whilst still being fittable through your hole! You can do this just as easily by measuring up your ply against the FRONT of the hole of course so you don't drop it inside your wall whilst measuring up!
I squirted No Nails glue around the perimeter of the plywood piece esp. the bits that would overlap with the plasterboard wall.
I fed this ply piece through the hole then, using the string, pulled it flush with the wall plasterboard. I held it in place whilst the glue dried with a pencil spanning the hole. Once dry, remove the string.
You now have the back supporting plate. Cut a small bit of plasterboard which is the same thickness or marginally thinner as that of your wall (skips?) to the same size as your hole or as near as poss. Glue this piece to the ply which now forms the back of your original hole.
You should now just have a narrow channel around the new piece of plasterboard which you need to fill with several applications of polyfilla allowing each layer to dry. You'd need a pointy nozzle to get it in! But once the top layer is dry, sand it back and voila! Fixed hole.
It sounds very complex but it's the way a professional would tackle it!