by Jerrod W
Jerrod, this has been discussed several times here on Hometalk - http://www.hometalk.com/?filter=popcorn+ceiling&search=posts
You can do a search here on hometalk when you are looking for something.
If its a sand texture a power pole sander used for Sheetrock spackle does the trick nicely. It can be rented at most home centers and uses a vacuum to pick up the bulk of the dust. But you still need to cover everything. Its hard on arms but not to bad of a job. If its popcorn then you need to wet and scrape. If its painted popcorn lots of arm scraping with lots of drop cloths to pick up the debris as it falls.
I can't tell much from your photo can you post a better photo or describe the ceiling in more detail?
probably easier to skim new mud,and sand to smooth
Depending on how it was applied....you can mist it with a water filled spray bottle and scrape with an angled floor scraper (you might get lucky)....this is one of the worst jobs going! We did one last year where they must have used a mortar mix for the stipple....took a week to do 4 rooms....we ended up using a combination of methods including a Porter & cable powered sander with a vac attachment....LUCK!