You don't say what kind of texture the ceiling is, but usually asbestos ceilings have a "popcorn" texture (which I always thought looked a lot more like cottage cheese than popcorn, but what do I know,) and if it was from the 50's maybe you even have the kind with the neato sparkles in the texture. Even without the asbestos issues, cleaning this type of ceiling is a real bear.
You have a couple of options, which I like best, and another option which I don't like real well, and don't recommend.
1. My first recommendation is to hire a painter to come out and "encapsulate" the asbestos ceiling by applying what amounts to a very thick coat of latex paint to the ceiling, usually with a sprayer. (Paint the rest of the inside of your home while you're at it.) This will help protect you from any potential "furniture moving-scraped the ceiling on accident-now I have all these fibers snowing down on my shoulders" accidents from being as bad for you as they otherwise would.
2. Hire an abatement company to come out and remove the asbestos altogether, then start over from the drywall or lath and plaster base to create a new look and an asbestos free ceiling. (This option is EXPENSIVE and not necessarily worth it, but I don't recommend trying to do it yourself.)
3. I don't recommend "Blowing" the ceiling clean, as the compressed air will only blow asbestos particles all over the place, which is THE WORST thing you can do. Vacuuming can have the same if not worse effect. Damp wiping a popcorn ceiling is almost impossible.
Before you fret about all of these things, call your local health department and tell them you would like to have your ceiling tested for asbestos. They will tell you what kind of a sample they need and how to take the sample safely. The test won't cost a lot, and you can make an informed decision from there.