If you're sure the tile is from the 70's, then there's DEFINITELY an asbestos 'hazard'.
Here's a link that gives more info on the subject of asbestos in the home. The key to its removal is relatively simple. Try to remove it ALONG WITH whatever it's glued to. Usually, there's some sort of underlayment. AVOID cutting ANYTHING with hand or power tools. The dust poses the RISK to exposure to asbestos! Use crow-bars and hammer claws and a cat's paw to help remove the underlayment. When you get outside, THEN you can put on a mask (rated for asbestos use), and cut the stuff up in pieces. OR, you can try to bend and break the pieces. (Of course, I'm talking about the underlayment AND tile, together, as 1 'piece' of flooring when you break it up.) You may not have to do this if you have a dumpster. If it's going into the trash, you need to call your Hauler to see what 'size' they want it to be (at a MAXIMUM.)
Once you've removed the underlayment and tile, you go from there as to what you're going to install NEW. Depending on the flooring will dictate what you put down next for 'underlayment'. My best to ya and hope this helps.