Just go over it with 1/2" drywall. Be sure to premark studs so you can screw into and use long enough screws. Finish it smooth.
Here's some help for you. It's a messy, tiring job but you can do it. I have, more times than I like to remember. :)
When I had mine removed, a sample was taken to a commercial lab to check for toxicity, common in popcorn ceilings. If so, it must be removed commercially. The workers had to wear the hazmat suits because in removal it gets into the air. The debris goes into a large vacuum truck. It's not a DIY job. We then had the ceiling remudded. I don't know if it would be smooth enough after removal for a flat finish.
We removed ours by wetting a section and scraping it off. We had to cover everything and it was a big mess but it came off. It left a textured but flat ceiling and we painted it. Our neighbor did it later and duct taped the scraper to the wide vacuum attachment of a wet/dry vacuum hose and saved himself the big mess. I wish we had thought of it! Hope this helps, Donna. Our ceiling was also painted and came right off.
Hi Donna: Here's a site I found that you may find helpful: