The easiest way to remove acoustic,(popcorn), ceilings when they haven't been painted is to lightly dampen it,( garden type sprayers work well), let it set for a few minutes, and scrape away. You won't be able to recover the texture underneath assuming it was sprayed over the existing. The most important step being 1970's is that you take a half dollar sized sample down to your local hazmat abatement office and have it tested for asbestos.. Typically it's free of charge or a minimal amount. If sprayed over the existing, it's possible it was "popcorned" in the eighties or later, but to be on trhe safe side, it's always a safe bet to have a smaple tested.

A damp sponge in a small area is the best way to find out. I remove a lot of popcorn in my remodels and the last thing a client wants is another texture. They are wanting smooth flat ceilings these days and so I skimcoat and sand.

gdeann-
By all means get a test done first on the ceiling, as sierraeast suggests. Here is a link on the risks and procedures related to removing popcorn ceilings which you will want to be aware of before ripping into a ceiling of unknown composition. Not all popcorn ceilings pose an asbestos risk, but many do, and an improper removal is an excellent way to thoroughly contaminate your house.

Here is a link that might be useful: Removing popcorn ceilings

I would definitely NOT remove it by scraping it. It's much better to drywall over it or skim coat it.

You want to what? Remove the popcorn and preserve what is under it? No, NO, a thousand times no. It will need to be either re-drywalled or skim coated to a texture.