How do I patch holes in drywall?

It depends on the size of the hole. Here's a link for you, Vivian:

https://www.thisoldhouse.com/how-to/how-to-patch-holes-drywall

On the tv show Shark, someone bought the idea of different size patches, ready made. Look on Amazon, ask Lowes. etc..

As stated elsewhere, the size dictates. However, I have a tip for the finishing. Most people recommend sanding but if you will use a large sponge wrung to barely damp it will finish as well as sanding and no dust everywhere.

As all noted it depends on the size of the hole. It also matters with what kind of wall your working with although not as much. A plaster and lath wall can be patched by cleaning up the hole and cutting it into a square then plastering the open area. You should do several thin coats allowing them to dry in between for a better result. Or you can buy sheet rock and cut to size and fill in hole then plaster edges. If it is only a sheetrock wall The same basic idea is used but you have to have something behind the hole to keep the replacement piece from falling through. My husband glued a piece of lath on the back side of a small hole and then put the sheetrock up against it. I'm sure some of the patch kits would give you instructions on how to do it too.

My Uncle John, a pharmacist, had a second life has wallpaper hanger, plasterer and painter to our family, comprised of the four sisters broods. The patch in this article with the paper edges is close to his go to for holes. Cut the damage square, cut a patch two inches wider all around. Break off the plaster at the edges. Instructions for this and other patches found here: https://www.lowes.com/projects/repair-and-maintain/patch-and-repair-drywall/project