Here is another method, if your hole is a bit bigger.
Cut out the hole square. Fasten in backing along the edge so you have a surface to fasten the patch piece. Plywood pieces work good for this. Cut a patch piece and fasten it into the plywood pieces. If the hole is larger than a foot square, you should probably tape and then finish. For small door knob size holes, I usually don't tape since a crack does not occur in a small contained joint.
For more information on hole repair and steps for taping and finishing, go to
Drywall Repair a Hole in Drywall - Instructions