Lay a tarp on the floor under the ceiling tiles. This helps to corral not only the old tiles, but any dust and debris that come down with them.
Put on safety goggles, a face mask and gloves. This keeps you from breathing dust or powder from the tiles. Wearing safety equipment also helps insure that you won’t get cut or scraped by the panels, or by pieces that come off them.
Place a ladder under the tiles you want to remove. Relocate the ladder as you work to reach all of the tiles.
Slide each tile out of its framework, lifting it at one end and then angling it so the other end comes down through the opening. Pull it all the way out of the frame and drop it flat on the floor. If you have an assistant, hand it to him and have him stack the tiles to one side, out of the way. Repeat this process until all tiles have been removed from the ceiling.
Put some of the tiles into a heavy-duty contractor trash bag and tie the top shut. Don’t overload the bag, as it will be difficult to handle and may rip. Only put in as much as you can comfortably lift. Contractor bags are available in discount stores and home centers. These work well for bagging ceiling tiles because of their large size and they are significantly thicker than regular trash bags. Roll up the tarp and dispose of it as well.
Place the trash bags out with your trash or haul them to your local dump or landfill. Fiberglass ceiling tiles are normally accepted anywhere that takes other household trash, and can be disposed of in the same way.