Cut a small piece from a representative ceiling tile using a sharp knife. Wear a breathing mask and goggles when making the cut and wash your hands and clothes thoroughly. Seal the small piece of tile (a 1-by-1 inch piece is plenty) inside a freezer bag and label it if there is any question at all about the tiles containing asbestos.
Take the tile sample to your local county health department and ask them to analyze the tile for possible asbestos content. Unless the manufacturer guarantees that the tiles have no asbestos, assume any tile manufactured in the 1970s or before contains asbestos.
Remove all furniture from the room where tiles will be removed, assuming the tiles contain no asbestos. Seal all doors with plastic sheeting, tape over all possible openings.
Wear long sleeves and long pants, goggles, gloves and a respirator. Shift and allow tiles to simply fall through a metal framework if the tiles are simply sitting on top of the frame. Put all tiles into plastic trash bags, seal and then double bag inside another plastic trash bag. Seal the second bag as well.
Tear tiles down using the claws of a claw hammer if the tiles are glued to a sub-ceiling. This will be a messy, dirty job. Make certain that you are wearing a good respiratory mask as breathing the tiny pieces of fiberglass in the ceiling tiles can be dangerous to your health. Remove all other people and animals from the house before the project begins.
Bag all tiles inside plastic trash bags and put each bag inside of another plastic trash bag (double bag) and seal both bags. Do not put more than approximately 50 lbs. of old ceiling tiles into any one bag.
Remove any glue and remaining pieces of old tiles from the sub-ceiling with your putty knife and a hammer. Insert the flat edge of the putty knife blade under the edge of a glop of dried glue and tap on the handle of the knife with your hammer to force the blade under the glue. Pop off all chunks of old glue in this way. Place all hunks of glue into trash bags, double bagging and sealing both bags.
Put old (non-asbestos) ceiling tiles (inside doubled trash bags) into the regular municipal trash pick up, following all rules in your area for labeling construction waste and follow any rules for total allowable weight.
Vacuum the room thoroughly with a shop vac then wipe down all surfaces with damp cloths, washing out the cloth as required to keep it reasonably clean, and then damp mop the floor to remove as much dust and other debris as possible before returning furniture to the room.