From ugly stains to peeling paint to sagging ceilings, you have a problem bigger than aesthetics alone.

So, the obvious first step is to find the source of the water intrusion and fix that. Only then does it make any sense to proceed with the plaster repair.

In my experience, there are several common sources for leaks.

Plumbing leaks. If you can fix plumbing, you are ahead of the game. Otherwise, bring a professional in and get it done right. This may result in a hole or series of holes in your plaster. This can be disheartening, but they are not all that difficult to repair.

Roof leaks. There is hardly an old house that hasn't been visited by this accident one or more times. Usually it is the ceiling where the damage shows up. If you are lucky, you may only have some stains or a little peeling paint. But you may also have a larger problem, like pronounced sagging.

Water coming thru the walls. When an exterior wall is masonry, like stone or brick, it can happen that water will wick through the wall and into the plaster coat on the inside. So you get bubbling of paint and powdering of the plaster, maybe even loosening of some of the veneer coat (outermost plaster layer).

Sometimes the root of the problem is defective rain gutters spilling water onto the wall. On wood framed walls, water can leak in around windows sometimes, showing up as stains, flaking, etc.

Now, about remedies.

First of all, as a do it yourselfer, you can do a perfectly adequate job of repairing your plaster using drywall compound and drywall tape. If you do it right, and you have dealt properly with the water sources, your plaster repair will last. You really don't need plaster to repair plaster.

You can use all-purpose drywall mud, or "hot mud," a setting type compound that is tougher than regular mud. With hot mud, mix small batches. When you have completed one step, clean your tools and pan thoroughly before you mix a new batch.

Stains and peeling paint are simple to remedy. Scrape or wire brush the area, and then wipe down with a damp sponge or cloth. You have to remove all scaling material and powder. When that has dried thouroughly, paint on a stainkiller to lock in the stain and provide a tight surface for the compound to stick to.
Apply paper drywall tape to any cracks and give them two successive coats, at a minimum.

Larger holes require backing. If there is no place to fasten a patch, you have to put in backing. 1 X 4 boards or plywood strips can be screwed in place and thin drywall screwed to it. Shim if necessary first so the drywall is level with the surrounding plaster. Fill around the edges with hot mud and tape the whole perimeter. Skim coat the taped edges until all is flat.

If the plaster is sagging, you will have to remove it and replace it with thin drywall as described above. Over wood lath, this is pretty easy. If your plaster is the kind with gypsum style plaster lath, and more than the veneer coat is sagging, saw out the sagged area and replace with drywall, etc.

On exterior masonry walls, the water problem may be solved by a thorough cleaning first, then the application of a special sealer. It might be good to consult with a professional. Replace any defective gutters. Then, inside, scrape all loose/powdered plaster. Wipe off dust, etc. Dampen depressions and fill with one or more coats of hot mud as needed.

If you can repair your damaged plaster yourself, you have gained valuable experience and saved yourself money in the process. And ... you get to admire your handiwork!