How should I replace a 12x14 drop ceiling with studs and drywall?

You could cover it with styrofoam tiles-https://www.hometalk.com/diy/floors-ceilings/covering-up-a-very-ugly-ceiling-with-styrofoam-ceiling-tiles-29254181

well the drop ceiling must be fastened to something. What is up there above the dropped ceiling?

Well a lath ceiling would have to be plastered. That would be lovely. Is it your room that is 12' X 14'? You want only an 8' ceiling although it could be 10' with all that extra room for storage. O.K. you will have to somehow frame it so the sheets (4' X 8') of wall board can be fastened. This is a question for a home renovator. But if you wanted to just do the ceiling at a 10' height you could nail the sheet rock to the already existing joists.

Technically you'd frame the ceiling like framing a wall. The perimeter 2X4's would be screwed to the walls. Then put up the drywall. But why would you want to do that? I would remove the drop ceiling and all the rails. Patch any holes in the walls. Use 1/4" X 4'X10' drywall on the ceiling, crown molding in the corners (so no patching there). Would look amazing. Georgia Pacific made 1/4" thick drywall in 4'X10' sheets specifically to cover popcorn or textured ceilings eliminating the mess of removal. The added 2' length makes for less joints to patch.

Hi,

I agree with all the above

How much clearance do you want to have in the room - floor to ceiling?

The reason is this, the best way to put new drywall ceilings over old is to use 3" x 1.5" or 4"x2" (75mmx35mm or 100mmx50mm) timber fixed to the existing ceiling as battens, which will stay flat and easily span the room, fixed at either 16" for 3/8" (450mm for 10mm) drywall, or a maximum of 24" centres for 1/2" drywall (600mm for 13mm drywall ceiling boards)

The total depth of loss of ceiling height will be around 2.5", so on a tall ceiling it's hardly noticeable.