Easiest way to patch a large hole in drywall?

For anything bigger than a fist, a patch needs something behind it to screw into. Cut the damaged bit out into a neat square, slide a couple of wood battens inside the hole and screw them through the wall either side. Cut a piece of drywall to fit the square, screw it to the battens, then tape the seams and skim over. Thin coats, each one feathered a few inches wider than the last. Most people slap one thick coat on and that's what cracks and shows through paint. In a cold room that dries slowly I'd use a setting-type compound (the powder you mix) for the first coat, it hardens chemically instead of waiting on the air.