Professor wrote:
Here are some images so you can see what I'm talking about

http://mysite.verizon.net/iunknown/Ceiling/index.htm

This is an old house and I'm not even sure how they made the ceiling because
I don't see any screws or nails holding it up. It looks like some plaster
was applied to the lattice and then sheetrock was stuck to it but it's
probably screwed in and I'm not seeing the screws.

I'm guessing to fix this I would cut out a square that encompasses the
entire hole then screw in large piece of sheet rock and use mud to cover and
smooth it out and sand it.

does that sound right ? Any recommendations on materials needed?

Thanks alot !!!

Yeah, this could have easily been my home a few years ago. Don't try
to repair the paster. The keys (pieces of plaster that smoosh up
between the lath and hold it all together) are long gone.

Proper way:
Do what grandpa said

Improper way:
Screw 1 x 3's directly through the plaster into the ceiling joists
and attach the drywall to that.

Whatever else you do, make sure the source of that leak is fixed.

BTW, clever Verizon user name. Everything implements iunknown.