It probably will never look perfect - i.e., seams will show through the paint, etc, but if you still want to try it, start by cleaning the wallpaper really well. TSP and thorough rinse. When dry, prime with a really good primer before you put on finish coat. Allowing extra time to dry/cure is probably a good suggestion before using the space.
Yvie. Don't paint won't adhere properly. Aloha!
Yvie: Take a look at these links and see if it is something you would feel confident in doing. Good luck on your project!!
How old is the vinyl wallpaper? New high-end vinyl wallpapers are vastly different from older versions. Although it might be 'possible' to paint over any vinyl wallpaper, it is not recommended. It will not adhere properly, or cover evenly, and will be an even larger mess to try to remove. If you don't like what is on the walls now, do it right, and remove all the old stuff first.