As Ron stated, removal is very messy, but very easy.
First thing is to make a tent with tarps all around the home. You want to keep the dropings from tracking and falling around the home. This is very messy, I cannot stress how messy it is.
If you walk on this and do not do a good job in tarping, this will grind into the carpet and have more of a mess.
I would stress to do one room at a time. Meaning scraping, removal, cleanup and re texturing and painting.
What I have done in the past is to saturate the popcorn with water until it turns a dark gray. Then with a long handled tile scraper, I will just lightly scrape the stuff off then immediately wet vac it up. With the stuff wet, it cuts down on dust and keeps the stuff in big wet gooyey gobs.
What you have to be careful about is not to scar or scrape the paper sheathing off the existing wall board. And you have to make sure that you do not get the ceiling too wet. After scraping down the ceiling in one room and after removing all the debris, I then set up fans to circulate and ventilate the room so that the ceiling will dry out.
Now, popcorn is used as an asthetic ceiling and one to HIDE imperfections. If you have imperfections, then you have a completely new can of worms to address.
Are you sure you are ready for this task and possible surprise? Remember, if you remove the popcorn and find the imperfections too much to bear and too bad to fix, you may wish that the popcorn was still up there.
There is no turning back once you do this.
Wear face masks and wear eye protection when doing this.