Walls and Ceilings - Repairing a garage ceiling after a leak

We had to have our whole flat garage roof replaced this spring because it was leaking through into the garage. We now have lots of water damage on the ceiling. Mainly along the joints of the drywall. They are puffed out and the tape? or something is peeling in some spots. What is the best way to repair this. I had someone give me an estimate of 500.00 which seems a little high. I think I can just chip off whatever is peeling...but I don't know how to fix the puffy spots. I have used joint compound before on a wall that was damaged by wall paper removal..would it be the same process....what kind of sand paper do I need to use??

As long as the sheetrock is still sound all you have to do is remove what is loose, retape any tape joints that need it and apply mud as necessary to make smooth. 80-120 grit sand paper works best.