A live octopus can be bought both in aquarium stores and ordered online to be delivered through the mail. Depending on whether you are hobbyist or a scientist, you can buy an octopus from various suppliers. Certain sellers only carry certain species of octopus, as well.
It is important to research the species of octopus you would like in order to determine which retailer to purchase through. Often, smaller octopuses cost less and are less expensive to ship, since many mail-order shops price their octopuses based on size. Try searching online for mail-order stores or for aquarium stores that are local to you.