Hold on there, don't take a sawzall to the tin if you plan on saving it. What you're looking at is "Restoration" work, and is going to require some patience. The tin is nailed along the seams, probably with small finish nails. Carefully get under the seam with a thin scraper blade or similar tool, and try your best to pry it a little at a time, moving evenly around the tin until you can pull the nails.
After you've removed the tin from the area in need of repair, scrape away the plaster with a pry bar or similar heavy tool. You might not need to remove the wood lath (assuming it's wood lath), but if you do have to, save a few pieces to fir the joists if needed.
After the plaster is removed you should be able to determine what thickness drywall you will need, most likely 1/2" or 3/8". whatever the case, once you get it to the proper level, mud and tape it as you would any plaster patch.
While the tin is down is a good time to remove the old paint. A non-toxic paint remover, such as Peel-Away will work well. Then wire brush and or steel wool away any rust. Prime with a rust inhibitive metal primer. Re-attach the tin using the same size nails you removed from it. Prime, paint and if you still have any energy left, pat yourself on the back for doing a good job.
Gotta luv them tin ceilings!