Polystyrene ceiling tiles are glued in place and, as such, are tedious but not difficult to remove once they start showing signs of wear. They crumble easily and can be removed with little more than a dull scraper, as long as you're willing to put in the time required. Keep in mind that polystyrene tiles are often installed to conceal ceiling damage, so you're likely to find holes, water spots and other signs of ceiling problems you may not have known about previously when removing polystyrene tiling.
Remove as much in the way of furniture and accessories from the room as is reasonably possible. Cover everything remaining---including the floor---with tarps or plastic sheeting to help contain the polystyrene mess you're about to create.
Start in the least prominent corner of the room. Set up a step ladder.
Climb the ladder and use a dull paint scraper---held at a shallow angle to the ceiling---to scrape the polystyrene tiling away from the ceiling surface.
Move the ladder as necessary to continue working across the ceiling, scraping the polystyrene tiles off as you go. It's always better to move the ladder than to lean far out from the ladder in an effort to reach farther and risk falling down.
Use a wallpaper steamer to loosen the glue that held the tiles in place, then scrape it away using the same scraper you used to remove the tiling. Work carefully to avoid damaging the ceiling surface.
Gather up the tarps or plastic sheeting once you're done, bundling them together to keep the polystyrene debris from spreading, and dispose of them in the garbage.
If you don't have access to a wallpaper steamer, try using a fabric or clothing steamer instead.