I have a large hole where a TV wall mount once was (I believe the hole was used to run power and coax cable to the TV). I have since moved the TV and would like to patch the hole. What is the best way to do this?
They sell dry-wall patches for this purpose.
Correct way to do it as instructed on 'Canada's worst Handyman':
Same process works for larger holes and also on the ceiling which can be tricky.
Use a drywall repair patch. They are cheap and easy to find at the big box stores.
And here's a video on how to do it: http://www.youtube.com/watch?v=qvtoikKG318
There's an alternative to @dilbert789's solution when you're dealing with holes this small:
I would still use @dilbert789's answer for larger holes, though, or anything in the ceiling, but I had a few incidents of wrestling with strapping when repairing similarly sized holes (fists, doorknobs, etc.), as you need to hold the new reinforcement, the screwdriver, a screw, etc, which gets difficult to juggle for one person.
Do you have a stir stick for paint handy? Slap some thick glue on the ends and glue that in as your backer. No need for screws on such a small hole.
If you're daring you can just mud the inside lip of the hole and squeeze a plug cut to shape in there, too. But then you run the risk of it tilting all funny.
Dry wall patches like everyone has mentioned are ideal for these small jobs. Otherwise, cut out a slightly larger square around the hole and do the method Dilbert789 mentioned above.
If anybody needs help with bigger repairs and happen to be in the Milwaukee area, feel free to hit up my team. We do drywall repairs large and small: Milwaukee Drywall Pros