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 !!!