Q: How do I clean and cook octopus?

A: The best way to clean an octopus is as follows: First, turn it inside out and pull away the entrails, the plastic-like bony sticks, and the stomach sac. Second, discard all of the items you've removed, turn the octopus right-side out, and find the beak in the middle of all the tentacles, and cut it away. Third, wash the octopus well.

From here -- unless you're dealing with a baby octopus, which is usually tender enough to eat on its own -- you're going to have to tenderize it so it's not unpleasantly chewy. There are a few methods for this:

1) The tedious and impractical: Banging it repeatedly against a rock.
2) The scientifically implausible but apparently viable: Simmering it with a cork for an hour and a half.
3) Reasonably possible: Roasting it in a cool oven for two hours.

Once it's good and tender, it can be grilled, braised, sauteed, or even served as ceviche