Small Drywall Holes

Pour some plaster of paris dry compound in a container you don't like that much.  Add about a third as much water as there is compound and stir around.  If you can, use a container that is long enough that you can lower one end to hold the water, and have the plaster powder at the other end.  This way you have more control of the water not getting into the plaster powder until you're ready.

Mix the water and powder together to get a peanut butter consistency.  Work quickly because the plaster will dry in a few minutes.

Push the mix into the hole or crack with a trowel.

Use 2 putty knives. Pull the putty down to the edge of the knife so that you can push it in more easily. It has a tendency to ride up toward the handle as you apply it and you have more control when it is at the end of the knife.

Do two applications. First application, you should indent it with your putty knife so that it mushrooms inside the wall and creates a better bond. Go smooth with the second coat.

You can't sand plaster, so make sure you scrape off any plaster excess protruding past the wall while it is still soft. Use a clean knife to scrape the wall.

Don't paint for 24 hours.

If the hole is bigger than 2 inches: A 2 inch hole can be filled without backing. Bigger than that, you can use painter mixing sticks as a way of creating a lattice backing. You can pry them into studs (between the stud and the inside of the wall) or screw them in. You can snap them with your fingers or cut them with a utility blade or saw. You can also use 1 x 3 strapping and screw it right through the wall then remove the screws when the patch is hard and fill the screw holes with plaster. The most important thing when filling a hole is that you use enough plaster to touch at least 3 sides of wall or strapping. As long as you do this, it won't fall out (if it's peanut butter consistency). The beauty of plaster of paris is that it dries so fast, you can do a big patch in small steps every 3 minutes or so. Each step makes a stronger patch. You have to work real fast though.