Get a PADI, BSAC, NAUI or SAA certificate so that you can go scuba diving. Octopuses live on the ocean floor, so unlike Oswald the blue octopus of television fame, you have to go to where they are to find them as they won't come to you.
Go to an area where you will find octopuses. National Geographic reports that some octopuses are found in tropical waters others in cold. In the Americas, this means from about Florida south to French Guiana. The largest breeding grounds, however, are in northern Europe and South East Asia.
Ask the locals where to find octopus. Individuals who fish commercially are particularly knowledgeable about where to look as octopuses sometimes get caught in their nets.
Arrange to go scuba diving. Ask around and find out which dive operation specializes in going where you might be able to find an octopus. Ask if they have any underwater photos of the area with octopuses in them.
Be prepared to wait. Once you are in the octopus area, be patient until you find an octopus. Remember that one of the strongest characteristics octopuses is that they blend in so well with their surroundings, making it very difficult to spot them.
Learn to stay very still. Octopuses have very good eyesight and they will be able to spot you. When you find them you are going to have to play by their rules as otherwise they may shoot their dark ink and disappear.