How much does it cost to fix a doorknob-sized hole in drywall?

Definitely worth attempting as a do-it-yerself project, but don't expect perfect results immediately. Drywall and joint compound (mud) are exceedingly simple to work with if you're a veteran, but exceedingly difficult to manage if you've never held a trowel or applied mud to a wall. Go slow! Expect to make mistakes. Experiment with applying mud to a blank portion of drywall first. Go easy with the sanding, and anticipate a substantial amount of dust. Lay dropcloth in the vicinity to catch the dust and protect the floor or carpet. Of course, these remarks only apply if you're planning a professional-quality repair that will be invisible to the eye. This will be preferred by your landlord, needless to say.  more

Your local Ace or Home Depot should carry a drywall patch kit for $10-$20. Some are made specifically for doorknob-shaped holes, as what happened to you happens to a lot of people. It's an easy job to do with very little in the way of labor if you are a DIY type, but Bencherman is right in that total job time is lengthy because you do a few minutes worth of labor and have to wait until the next day to come back to it. Zenmaster also has a good point. You can go the really cheap route and use whatever happens to work. I recall patching a wall by gluing cardboard in back, filling the hole with toothpaste, waiting for it to dry, "sanding" with a damp washcloth, and adding a little paint. (This was in college. We didn't want to get charged for repairs and were too lazy to do it properly.  more