I am surprised you have not had responses to this post. You might try reposting. You could also try DIYChatRoom.com. If you have no other options, consider the following.
I don't have much relevant experience (where I live, the only to possibilities are drywall and wood paneling) but I recommend you try to figure out what the ceiling is made of. If there is attic space above, see if you can get a look from above. It might give you an idea what the material is, and possibly why it is sagging. Scratching a SMALL hole through the surface (from above or below) should tell if you have drywall, paneling, or something else. If it is some kind of paneling you should be able to nail it into place. If drywall, you should use drywall screws, being very careful the screws do not break through the surface paper (your hardware store will have a driver attachment for your drill that will do that). If the material is something else, you need advice from someone other than me (actually, you need that anyway but no one else has responded). You will need a stud sensor to determine where to place nails/screws. For either, you will need to push it into place before securing. Something like using a car jack to push up a "T" made from 2x4s, with the cross piece at least 48" wide, should do it. Based on what you saw from the attic or using the stud sensor, be sure your T is perpendicular to the studs; if parallel you could do serious damage. Drywall and paneling normally come in 48" wide sheets so pushing up one but not an adjoining sheet would likely cause a crack between the two, so proceed cautiously and watch closely. With either, you will need to patch the nail/screw holes.
Was the ceiling sagging when you bought the house or is this new? Especially if new, this could be a very serious issue and you should get immediate, qualified help. Personally, I would call a professional drywall company but I would think a handyman service should be able to tackle this. Also consider hiring a home inspection. They are typically done at the time the house is sold and would give you a lot if info about the condition of your house, what other repairs might be needed that are not apparent to you, and what priority to give them. The inspectors opinion about the ceiling would be gravy.