When drywall is wet, it's softer to the touch than when it is dry. An easy way to test for wetness is to press a hard tool, such as a large screwdriver, against an area of drywall you are positive is not wet. Then use the same amount of pressure to push the tool against the area you suspect is wet. If the suspicious area mars more easily, chances are it is wet.
Water causes drywall to destabilize, so large amounts of water can make drywall warp or bow. Typically, damaged drywall will retain the warped shape after it dries. If this happens, you must cut out the warped portion using a utility knife. Replace the drywall with a fresh piece but only after the area has been dry for several days. If you trap moisture within the wall, mold may develop later.
Water often causes a rusty-looking stain to spread across the paper surface of drywall. Typically, it is darker than the surrounding area and has multiple rounded edges, like cauliflower. The stain will show through even multiple coats of paint unless you use an appropriate sealing primer. Most retail hardware stores sell sealing primer specifically designed to hide water damage. Follow the manufacturer's recommendations for application and don't apply the sealing primer until you are sure the drywall has been dry for several days.
Mold can infest wet drywall quickly, so use large fans or dehumidifiers to remove as much moisture as possible from the flood area. If you notice dark mold growing on drywall, you must cut away the infected portions. Drywall is porous, so it's not possible to scrub mold away. However, if the drywall is painted, and the mold has not penetrated the paint, you might be able to use a brush and a bleach cleaning solution to remove mold. Hire a professional mold remediation contractor if the mold infestation is larger than several square feet.