There are repair kits at home improvement centers, but personally, I do it this way:
Cut the whole with a drywall saw so that it's cleanly-shaped (usually rectangular) and so that you can easily cut a piece of new drywall that will fit close to the size of the hole. Cut some 1x3s that will fit along the edges of the joint. While holding each 1x3 in place, drive drywall screws through the
old drywall into the board. Two or three screws will be sufficient to hold the boards in place.
Take a new piece of drywall the same thickness as the old drywall. Try to cut it as closely as possible to the size/shape of the hole you're trying to patch. Drive screws through this piece of drywall into the 1x3s that you just mounted.
Get some premixed drywall mud and a drywall knife (6 to 8 inches wide is probably best. You can use a 3 or 4 inch blade for this job). With the drywall knife, fill the gap with drywall mud. Because of the 1x3 holding the drywall together, you really don't need drywall tape (this may be controversial), but if you wish, you can put drywall tape over the seam.
To tape, put a thin coat of drywall mud over the seam and push paper tape into the mud. With your drywall knife, squeeze out the excess mud from the sides, until the drywall tape is sitting firmly against the drywall. Put another coat of drywall mud over the top of the tape and with a drywall knife, smooth it while extending the mud out far enough to make the tape not noticeable.
When the drywall mud has dried, sand it smooth and put on a second very
thin coat of drywall mud to smooth out the imperfections. When the second coat has dried, sand lightly, prime with a sealing primer (it doesn't need to be oil-based), and paint the wall. If the wall isn't smooth enough after the second coat of mud, you can put on a third, fourth, etc. Since you're inexperienced, you'll probably need at least three coats of mud.
The hardest part of all of this is trying to match the paint.
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