- Sand off tops of "popcorn bumps" with rotary sander or multi tool (like bosch multi-x).
- Spray with vinegar and water.
- Use elbow grease and a scraper or hope this happens:
If the popcorn finish is fairly even throughout, and you can afford to lose just a bit of headroom, one method is to skim over it with thin wallboard (3/8 is generally available and 1/4 can be special ordered). This is put up in sheets and screwed to the underlying structure (which needs to be located with a stud finder or the poke-with-an-awl method). Then taping, mudding (filling the joints), sanding the joints and painting. Sounds like a big job, but usually less time consuming than taking down the popcorn surface.
A friend of mine removed the popcorn from the ceilings and it was quite the project / mess.
Water if it soaks through to the drywall can damage the paper on the drywall. If that happens, you'll need to cut out the damaged paper, prime, patch with a joint compound (finish the surface) then prime and paint
I would probably just try using a putty knife or drywall knife - 6 inches maybe? And scrape it off.
If you were gonna drywall over it like bib said, remove the old drywall first. Why leave it up there? Cut the corners, pull down the drywall / screws and re-drywall properly. Cost difference between 1/2 inch drywall and 3/8 or 1/4 is negligible and in the process, may allow you to run electrical for new lighting, ceiling speakers, etc...
I agree with Mario on the hesitation to use any liquids on drywall. If you don't want to replace the drywall (which is a good suggestion), then this would be my process:
After knocking off the loose popcorn with a drywall knife, I'd make a pass or two with a screen sander on a pole, and then one final pass with a wide drywall knife to knock off any high spots. Then clean the surface of dust and apply a layer of premixed joint compound over the entire surface to cover all the blemishes. Keep the layers thin and you may consider adding a little water and dish soap to the mix to make it apply smoother (tip from Shirlock). Use a wide drywall knife and do your best to avoid any ridges. Lightly sand the result with the same screen sander on a pole, fix any small blemishes with a sponge sander, cleanup the dust, and paint.
Realize that popcorn is frequently used to hide blemishes and a poor quality drywall installation. So before applying the joint compound, I'd shine a light at a sharp angle to see your problem areas.