Painting- do I paint oil based paint over water based or water based over oil?
You must first determine whether the already existing paint (that is, if you’re referring to paint on your walls) is oil-based or water-based. Put some alcohol on a rag that’s not the same color as the paint on your wall. Then try wiping the paint off with the rag. If the paint dissolves, it’s water-based paint. If it doesn’t, then the paint is oil-based.
Now as for your question on whether you can use water-based paint over oil or use oil-based paint over water-based paint: if you’re using water-based topcoat to paint over oil-based primer, then you can expect no trouble with the result. Note that you must make sure the primer is totally dry before applying your water-based topcoat. Same goes for applying water-based paint over oil-based paint. Just make sure you sanded the surface. Painting oil-based paint over water-based paint however can become problematic.
If you’re talking about paintings, as in the artworks done on paper or canvas, then the general rule most artists follow is that oil-based paints go with oil-based paints, and water-based paints go with water-based paints. You can learn more about oil paintings and other mixed media paintings by visiting nickgwilliams.com.