How do I paint my floors with out taking out the old linoleum?

Hi Imogene, here is the link to other hometalkers that painted theirs. You can check them out.

https://www.hometalk.com/search/posts?filter=paint%20linoleum

Here's a video tutorial on how to paint over linoleum with chalk paint: https://www.youtube.com/watch?v=bN4Yis4fPbM

CLEAN the floor with your regular cleaner. Clean again with just vinegar & water. Let it dry completely (no tracking). PRIME it with Kilz primer made for Kitchens & Bathrooms. It prevents mold & mildew. Apply with a paint roller will be ok & let it dry overnight. Paint after 24 hours with whatever color you desire. You could even hand paint it if you're artistic. Let paint dry overnight. SEAL with Thompson's OR Mop & Glow heavily to create a barrier over your paint. Let it dry for another 24-48 hours. You're done.