I had to go through the popcorn removal to repair my ceilings. It's not something you want to do unless you absolutely have to.
Here's how I did it.
1) You must get plastic and cover the walls and the floors.
2) Get a deck sprayer or small spray bottle. Spray the ceiling until it gets dark grey and doesn't absorb water.
3) Use about a six inch plastic putty knife and scrape the wet popcorn off. Be careful not to gouge the drywall, otherwise you will be fixing gouges. Some people recommend a drywall knife, but I had the best luck with a putty knife with one chamfered edge. Put the flat edge next to the ceiling. This makes a big mess.
4) And, by the way, once you wet the ceiling, all of your taped seams will come loose. You will have to re-tape all of the seams and work the tape seams out far enough to make them blend in.
5) Any cault between your ceiling trim and popcorn texture will have to be removed. You will need to re-caulk.
6) Look your ceiling over good for any gouges or defects in the surface. The texture hides an awful lot of imperfections in drywall.
7) Apply a good primer, like Zinsser Bullseye 123 Stain Killer to the whole ceiling. One gallon should do a bedroom easily.