How can electrons form pairs while they should be repelling each other? Indeed, electrons are electrically negative, and two negative charges repel each other. Cooper gives the following explanation:
At a low temperature, when an electron moves, it slightly attracts the surrounding atoms. The reason is that the electron has a negative electric charge and the atoms a positive one, since the latter is missing one of its electrons (we should say "positive ions" rather than "atoms"). A negative charge attracts a positive charge. If a second electron appears at that moment, it experiences two atoms at a closer range than usual for a short period of time, and it will be pulled between them. Two atoms closer together create a more electricly positive zone, thus being more attractive to the electron. The second electron naturally follows the first due to the oscillation of atoms. This is called "attraction via network vibrations" (or "phonons").
At high temperatures, atoms vibrate more and the path of the first electron is obscured preventing the second electron from following it and forming a Cooper pair. This is why conventional superconductivity only happens at very low temperatures.
Be careful, these animations only illustrate how the movement of the atoms aids in the formation of a Cooper pair. But they are not realistic. If you want to be more accurate, you have to consider electrons as waves, and here, we can see that the electrons which make the best pair are those moving in opposite directions, rather than in the same.
