The best way to fix acoustic ceiling tiles that have fallen or have broken is to replace them. Periodically check the tiles to make sure that they are set properly in place and have not become damaged. Fixing them will require some time to remove a damaged tile, replace it with a corresponding one and set it in place.
Locate the Damaged Tile
A damaged tile is one that is cracked, chipped, or has a hole in it. It may also have water damage, which is a different issue that should be addressed before replacing the ceiling tile.
If the roof or ceiling has water damage indicated by the discoloration of the tile and smell associated with damp water you should immediately find the source of the leak. This could be from a broken or leaky pipe or some leakage coming from above the ceiling. Have the leak sealed in order to avoid a more costly repair later.
Remove the Damaged Tile
Remove the tile by simply lifting it upward and pulling it down until it becomes free of the tracks. Pull the tile downward in order to free it from the ceiling. If necessary, use a utility knife to score and cut the tile away from the ceiling.
Purchase replacement tiles that are the same size and style of the tile being replaced from a hardware or home improvement store. Most acoustic ceiling tiles are white panels. They are fairly standardized. In the rare instance where the tiles were a custom made item, you will need to locate the manufacturer in order to have a special tile created as a replacement.
Replace the Damaged Tile
With the damaged tile removed from the ceiling, place a new panel in its place. Slide the panel into the uncovered area left by the removal of the damaged acoustic ceiling tile. Push upward on the panel and let it rest on the ceiling tracks for a perfect fit.