You can start by removing the obvious, and then some. Don't just remove what you see as being 'bad'. Chances are that there's damage where you can't see it. Since water runs with gravity, you have to envision that if the 'upper' part of drywall is damaged, chances are the middle, and bottom parts, are damaged too. Take out the obvious, and feel and look behind to see if there's unseen damage. A mirror and some light will come in handy. You have to remove from stud-to-stud at a minimum. Since the studs are 1-1/2" wide, remove only 3/4" of drywall on either side of a stud when working between studs. If you remove the entire 1-1/2" from the stud, the NEW drywall will go in just fine but what's the drywall on the OTHER side of the stud being supported with?!
My best to ya and hope this helps.
PS: You might want to check around to see if you can find a moisture detector and see if it can see through drywall.