Scrape off the loose ceiling material (popcorn) using a scrapper or a spackling knife. If it is in a joint area (corner or around a skylight) you may need to buy some joint tape and some joint compound....Replace the old joint tape by buttering (applying) the joint compound behind the tape, place the tape into the coupound and smooth with the spacking knife (follow the directions on the joint tape and compound). The next step can get messy...If the whole left is a big one, use a spray textured ceiling repair (covering everything that you dont want to get dirty. I pin a drop cloth to the ceiling, leaving a little bit of the area exposed to blend in the new and old textured ceiling. That's it.