Summarize:

Get your supplies together before you begin. To fix a lath and plaster wall you will need:  A plaster patching compound A large joint or finishing trowel Sandpaper Coarse grade screws for wood and fine grade screws for metal. Choose screws that are 1-1/4" to 1-5/8". You will need to remove all of the damaged area while making sure to not expand the damage. Gently remove any cracked or loose plaster, moving out from the center damaged area until all the plaster you encounter is secure. Use sheetrock screws but if the lath is cracked add wide thin washers to the screws when screwing down the lath. If some of your lath is damaged so much that it will not hold up plaster, you will need to replace it. This is the rough in coat, so the surface of the patch should be a bit below the surface of the wall and does not need to be sooth. Allow this layer to dry for a bit, until the surface is slightly firm but not hard. The consistency of this layer of plater patch should be like peanut butter. This coat should stick to the first one but the goal here is to give the surface a smooth surface that is level with the wall. This layer of patching compound should be just slightly thinner than the one underneath. This will allow you to more easily smooth out the surface with you trowel. Sand the surface with 220 grit sandpaper if you did not get the surface smooth enough with your trowel. Getting a completely smooth surface with a trowel will take a lot of practice, so don't be discouraged if you need to do a bit of sanding on your first try. Matching texture can be very difficult since it is usually machine blown. However, you can also get aerosol cans of texture in home improvement stores. To texture patches stick a stiff stipple brush in plaster and apply to finished and dry patch. If necessary, after it sets up a little, trowel over it to flatten high spots. Always use a good primer or a paint plus primer on plaster walls, as it will protect the wall and saves on cost of finish paint.
Gather and purchase your materials. Remove loose plaster. Screw down any loose lath to the studs underneath. Apply your plaster patching compound to the hole. Apply a second coat with your trowel. Allow the patch to dry completely. Reproduce any wall texture if your walls are textured. Prime and paint your patch.