Coilovers work like this: A very thin-walled threaded sleeve slips over the strut, and in any decent kit, the sleeve is notched so it fits over the ear of the strut where the spindle mounts so the sleeve is locked in place and can't turn. Then a threaded collar goes onto the sleeve and threaded down onto it quite a ways. This is the bottom mount that the spring will rest on, and raising or lowering the collar lowers or raises the ride height, respectively. Then the spring gets slipped over the sleeve, then a top spring mount gets put over the strut shaft so that the spring is captured between the collar and the mount. That mount sits up against the caster/camber plate, and on good kits, there's a thin torrington-style bearing sandwiched in it so the strut/spring assembly can turn without binding the coils. Voila, coilovers. Now, when the strut gets compressed, the threaded collar moves up with it, and compresses the spring against the top mount, and the spring pushes back down against the threaded collar to re-extend the strut.
This way, the conventional spring is discarded. However, not all strut housings are the same diameter. Bilsteins are different than most others (larger, IIRC). Cheaper kits use the same sleeve no matter what, so one-size-fits-all, and then what happens? They make a loose fit in most applications, and you get a lot of "waaaa waaa, coilovers are noisy" posts. It pays to find a kit that's designed for your specific struts (hint: They won't be $159 specials) and no, you don't have to buy the struts with them.
