Clean off a small area of the wall with household detergent and water. If you don't plan on painting the wall soon, choose an area in an inconspicuous location, such as behind the couch as this test may alter the paint slightly. Rinse the area with water and dry it with a towel.
Soak a cotton ball or soft rag in denatured alcohol, shellac thinner or non-acetone-based nail polish remover. The rag needs to be a different color than the wall.
Rub the cleaned off surface of the wall vigorously in a circular motion with the cotton ball for about a minute. You only need to rub a small area about the size of a quarter.
Touch the area with your hand. If the paint feels soft, slightly tacky or comes off, it is most likely latex paint. If the surface remains shiny, it is probably oil-based paint.
Look at the cotton ball or rag. If some of the paint has come off, it is probably latex paint. The paint may look thick or gummy.