From www.cmmginc.com

The way that I've always seen them used it to insert the tool into the broken shell(it's a broken shell extractor, not a stuck case remover by the way) then insert a rod from the muzzle end of the rifle and tap the broken shell out of the breech end of the gun. See how that one part slides into the other and expands it, pull it back out so it's not expanded before you insert it into the broken case, then when you tap it it'll expand and snag the case and remove it. It's as simple as that.