As electrons move about a nonpolar molecule, it causes the molecule to be, for an instant, subtly either negative or positive. when a molecule directly adjacent to it does the same, which forces attract these two molecules together?

The negative charge distribution that surrounds the nucleus of an atom is due to the atom's electron cloud. As the electrons move around a molecule, it can make a certain position, for an instant, look negative when the electrons are on one side and when they are away from this side it can look positive. This can cause intermolecular attraction and is known as the London Dispersion force of attraction.