Octopus, squid and their cousins are known to scientists as cephalopods, which could be translated loosely as "a head with feet." They share an ancestry with more conventional shellfish, such as clams and oysters, though only the nautilus retains its external shell. Cuttlefish and squid retain a residual shell inside their soft bodies, while in the octopus it has completely disappeared. Cephalopods are just as sweetly flavorful as lobsters and crabs, but are trickier to cook because of their anatomy. Their muscle fibers are especially long and strong to compensate for the lack of a supportive shell or skeleton. That makes them naturally tough and chewy.

Most octopus available at retail stores and fishmongers are already cleaned, and are ready to be cooked. If you've purchased your octopus fresh and whole, cleaning is relatively quick. Scrub the tentacles with a soft brush under cold running water if they show any signs of grit or debris. Usually this isn't necessary. Sever the octopus' mantle just below the eyes, then make a second cut just above the eyes to leave the edible portion. Discard the eye section, and carefully pull out the ink sac and entrails from the mantle. In the middle of the tentacle section you'll find the mouth opening and the tiny bill. Cut around it with a paring knife, and push it out.

The only further preparation the tentacles may need is skin removal, if you choose to do so. The skin is entirely edible, with a gelatinous texture that lends richness to the liquid it's cooked in. If you choose to grill the tentacles, the skin will be all but undetectable when you're done. However, if you want to skin your octopus for aesthetic reasons, it's easiest to do after it has been cooked tender.

Very small octopus can be grilled for just a few minutes, too short a time for them to toughen. Most octopus require longer, slower cooking, which tightens up the muscle tissues but then tenderizes them again over time. The octopus should be simmered gently in water or a more flavorful liquid, such as wine or fish stock. Most require about 15 to 20 minutes of simmering per pound, but there's a lot of individual variation. When you can insert the tip of a knife easily into the thickest section at the top of the tentacles, it's done. Cool the octopus and rub the skin away with a clean towel, if you prefer. It can now be served cold, marinated for a salad or quickly grilled, as directed in your favorite recipe.