I see how I can stop the atoms, but in a real sample of gas atoms, I have atoms going all different speeds. If the laser was set to slow the fast ones, wouldn't it just blast the slow ones in the other direction, and so leave them faster and hotter?

You are exactly right! The hardest part to laser cooling was to figure out how to avoid hitting the slow atoms with light while hitting the fast ones to slow them down. Some very clever physicists figured out how to do this by using the idea that the color or the light is Doppler shifted by the atoms' motion.

I remember about the Doppler effect. It says that if an atom is going towards the laser light, it sees the light shifted to a bluer color, and if it is going away from the laser, it sees the light as redder than it really is. And the amount of the shift depends on the speed.

Right you are. So if the laser is just the right color, the Doppler shift of a fast atom will make the light look the right color for exciting it, and so photons will bounce off and slow it down. But if the atom is moving slowly, or in the wrong direction, the Doppler shift will be different, and the laser light will be the wrong color to excite the electron. In that case, the laser light just goes right by the atom.

Now it is even harder! I have to keep adjusting the color as the atom cools down.