I have coded an animation (in python) for three beach balls to bounce around a screen. I now wish to have them all collide and be able to bounce off each other. I would really a
Detecting collisions was covered well by Pax's answer. With respect to having objects bounce off one another, I suggest checking out the following links concerning elastic collisions, inelastic collisions, and coefficients of restitution.
EDIT: I just noticed that this was covered in another SO question, albeit not specifically for Python. You should also check there for some good links.