Remove loose drywall/plaster.
Cut a sheet of metal lath the size of the damage.
Wedge the lath, or fasten it in place around the edge of the damage. Fasten it to any wood, with screws.
There are 4 basic drywall finishing compounds, 20, 60, 90, +3.
The numbers are minutes until it's hard, except +3, which is purely air cure, and it is the final coat.
Using a 6" drywall knife, make a joint between the metal lath and the sound area of the ceiling using 20. Just use the ceiling to scrape the compound off the knife into the lath. Wetting the edge of the good part of the ceiling will help the 20 adhere.
When working with drywall compound, use a metal mud bucket. The bucket lets you clean the knife every time you load it.
Don't mix more finishing compound than you can use in about 1/2 the cure time.
Using more 20, cover the rest of the lath with as thick a coat as will not start falling off, but not past the surface of the good ceiling.
If there's still quite a bit of difference, > 1/4", use some 60 to get things evened out, more flat, and closer to the level you need.
For corners you use a corner knife/tool. It's a drywall knife on a 90-degree angle. Start forming nice corners now with 60.
For flattening the patch, use a 10" knife. It has a camber, so be aware, and look down the blade to see which way it curves.
20, 60, and 90 are not nearly as sandable as +3. But +3 must be applied thin. So, when your shape is pretty close, get out your drywall tape. Fiberglass mesh is thick, so it takes a few coats to cover it.
I use paper, because it covers in one coat. But you have to wet the paper tape. Put +3 where the tape is going on the wall/ceiling.
Press the tape on the +3.
Even out the +3 with a knife, 6" and corner knives work well.
Put +3 over the tape, and even it out.
Make sure you can't see any tape.
Let it dry overnight.
Coat it again, going for the finish coat.
But if you're not going to get it, just get closer. Try the next day.
Now you should be able to get a nice finish coat.
Let it dry.
Wet-sand where necessary.
For texture, you need an air compressor and hopper, or roller texture, which is very fine.
The last step is paint.
If you can work with plaster, this is a one day job. But most people can't.