If you just paint over oil-based paint with a water-based acrylic or latex paint, once it has dried, you will be able to scrape it off with your fingernail. A horrible realization after all your hard work!
Check to see whether paint is oil or water-based by dampening a piece of cotton wool with an acetone based solution such as nail polish remover. Wipe the surface and if any paint comes off, it is water-based. If nothing comes off, it is oil.
You can paint over oil with latex but you have to prepare the surface properly. Clean, sand thoroughly, clean again, then apply a water-based primer such as Kilz 2 or Zinsser’s Bulls Eye 123. When dry, apply 2 coats of good quality acrylic water-based paint.