First, remove everything from that room, pictures, and all wall stuff. Cover the floor, and install drop cloths on the walls. Seal the area completely and have everything that you can not move covered.
Now, tools you will need. I prefer a inexpensive deck sprayer that you manually pump up and one that has a fan spray design. Fill the tank up with water and some fabric softener. Now, start spraying the ceiling beginning at one corner and slowly procede to the end. Then come back to the beginning and start over. Keep doing this until the popcorn turns gray. You don't want it actually dripping as this will damage the skin of the drywall, but it has to be saturated.
When you think its ready, then have your long handled tile scraper that is a putty knife about 16 inches long and is attached to a long handle. You can buy this at a home center. I like this because it saves on your back and you do not have to use a ladder. But, a putty scraper will work. Just soooo slow.
Lightly skim the surface as to shave the ceiling. Do not gouge the drywall.
All this should fall off with ease and on the floor, be careful not to step on this and slip. It will be a big mess.
Now when entirely gone, let the ceiling rest or dry for about three days. Let it turn back to a light gray. When dry, repair any divots, now do whatever texturing that you have planned, then prime it. I would prime it before I textured and then also after. Then finish paint it. Should do it.
I for one hate popcorn, because of the dust it collects and the falling stuff and the only way to paint it is to spray it.