There's an alternative to @dilbert789's solution when you're dealing with holes this small:
- cut a rectangle of drywall about three inches larger than your damaged area in both dimensions.
- score the back of the drywall one inch in from each edge.
- break the drywall at the score line, and then remove the drywall from the paper.
- trace the drywall portion of the patch onto the wall, over the damaged area. (the part that's still solid, not the paper that's 2" larger on each side)
- cut out along that line.
- test plug for fit, and if necessary, clean up the edge some
- put down some drywall mud on the inside of the lip of paper.
- insert the patch into the hole
- mud over the edges
- let dry, sand, and paint.
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.