When you find an Octopus, very slowly move towards it and maintain slow breathing and good buoyancy. Sudden movement or a blast of bubbles will scare them. Then, ever so slowly put your hand close enough that it can feel the heat from your hand (Maybe 6 inches or so). Once it feels your heat it will place one tentacle on your hand and test you out. Over the course of a few minutes it may then put more tentacles on you and eventually come out and attach itself to your arm. It does this to absorb your body heat and is also showing its trust at this point. Once it does this, you own it and can play with it until it grows bored and swims off.
I have seen this a couple of times and watched as it was passed from person to person.