Here is how to paint a styrofoam ball without getting paint all over your fingers!
Take a wooden skewer and stick it into the styrofoam ball. Hold the skewer with one hand and paint the styrofoam ball with the other.
When you have finished painting, push the other side of the wooden skewer into a Styrofoam tray for example, and let dry.
For smaller styrofoam balls, use a toothpick and proceed in the same way!