Judge the tenderness of the octopus by pushing a knife into one of the tentacles; if it easily pushes into the thickest part of the flesh, it's cooked.
Octopus contains a lot of moisture, some of which can be removed by brining or sun-drying to make the flesh more tender before grilling, barbecuing or pan-frying. Without removing some of the moisture from the flesh, the octopus will take on a chewy and rubbery texture.
This step isn't always necessary though – some methods embrace the springy texture of octopus flesh. For example, octopus can be simply marinated and enjoyed in a carpaccio style, used in sushi or deep-fried in a takoyaki batter for an enjoyable, crunchy texture.
Octopus has a very delicate flavour and dressing it with some good olive oil and seasoning it well is often enough. A popular way of introducing extra flavour is by cooking it over the hot coals of a barbecue or an ocakbasi grill, introducing a charred, smoky edge.
For inspiration, look to Mediterranean flavours which would typically get paired with seafood such as lemon, fennel, chopped parsley, tomatoes and white wine.