Stethacanthus resembled modern sharks to an extent, except for its outrageous dorsal fin - the shape of an ironing board - that it seems was part of courtship display as it is found in the males only. The top of this fin was covered in rough, tooth-shaped scales that match a patch of skin on the Stethacanthus' snout. Was this supposed to mimic a huge mouth and make the creature appear more frightening?
Stethacanthus tended to patrol shallow coastal waters on the lookout for food. It ate small fish, crustaceans and cephalopods (eg goniatites).
There's evidence Stethacanthus may have been migratory, returning to particular places to mate and give birth. It could certainly swim quite fast, although not quickly enough to evade a hungry Dunkleosteus.