If the lath behind the plaster is sound, you can patch it with new plaster.
Apply a coat to cover the hole. Use an old fork to lightly scratch a criss cross pattern in the repair. This will give your second coat a base to grab onto. You need to do two coats of patching plaster and a final coat of drywall spackle before then you can repaint.
The third common problem with plaster is loose or sagging plaster. What happens is the little keys or blobs of plaster that hold it to the lath behind have broken over time and the result is this loose sheet. To repair these areas you'll need some plaster washers and long screws that will pull the plaster back into place.
This area will need replastering, sanding and then paint. Easy how to's for plaster repair.
