It is possible to take the little shoots, cut them carefully and place them in individual little pots. Baby spider plants. When you do this, be careful that you don't damage the little shoot in anyway, or you won't have much success. They are generally fairly hardy plants, though, and it isn't completely necessary to remove the little sprouts either, it's fun to have billions of them growing everywhere.

When you transplant them, follow the general rules for transplating little plantlife, and keep a close eye on it at first. It might needed a lot of water at first, but not too much, use common sense, or a soil moisture monitor.

I've noticed that spider plants do extremely well when placed just off to the side of windows, so it isn't direct light but still a good amount. It's also a good idea to make sure you never let them dry out because the shoots growing down off the long tendrils will die easily if you don't keep it watered and healthy. They'll probably be the first things to go, actually, and that makes for a not so attractive or happy plant.