The first step is to prep the area by removing any loose or flaking plaster. Use a cold chisel and and ball pein hammer to chip away the damaged plaster and us a scraper to scrape away excess debris. Take care not to hit too hard with the hammer as it could damage the wood lath behind the plaster.
This process might make the hole larger, but will give you a clean area in which to apply the new plaster.
Once the surface preparation is complete, mix up only the amount of plaster needed for the repair. Follow the instructions on the packaging to ensure the proper mixture. Mix it to the consistency of cake frosting.
Apply the mixture with the 10" wallboard knife and spread a 1/4"-inch layer over the hole. Cross-scratch the first coat as it begins to set to allow the second coat to adhere well.
If needed, apply drywall/plaster tape to the wall to fill in larger, bumpy areas. First, apply a thin layer of plaster or joint compound and then apply the tape. Apply more plaster or joint compound mixture over the tape and use the drywall knife to smooth the surface until it's even with the wall, pressing to remove pockets of air and plaster/drywall mud from beneath the tape.
Once the first layer has dried, apply a second layer. Apply another 3/8"- to 1/4"-inch layer and cross-scratch as you did the first time. Allow it to dry thoroughly before you continue.
After the second layer has dried, mix joint compound according to the manufacturer's instructions and apply it very thinly using the 10" wallboard knife. Blend the layer into the wall and allow it to dry.