Repairing a Small Hole in Drywall

OK, this can't be any easier. Measure the hole size you're going to patch, then go to your hardware store and buy the appropriately sized adhesive mesh / metal drywall patch.
A good brand is Wallboard Tools Wall Patch

and it comes in a 4", 6" and 8" patch size (although an 8" is larger than I'd recommend for this patch).

Once you get the patch, just peel and stick.