This beautiful creature is very dear to my heart! I have named him Rorschach (Inky for short), since I am also interested in the field of psychiatry and I thought it was all too appropriate (though he/she-for the sake of simplicity, let's say "he"-has only inked once since arrival).
What can I say about this incredible creature? It is debatably the most intelligent invertebrate out there, and it shows. Inky lives happily in a 30gal tank mostly by himself. It is especially set up with low lighting and lots of live rock hiding places, plus some PVC tubing at the bottom for him to sleep in (since they are primarily shy, nocturnal animals, you will find him mostly in a PVC tube during the day). He comes out when he is hungry, and boy does he let me know! He does things like pulse color rapidly, wave his 8 sucker-filled legs at me,
or even squirt water out of his tank just to get my attention.
I feed him about one small thawed shrimp a day, on a long stick with a toothpick at the end. He occasionally also takes treats of live goldfish, but since they are freshwater fish, they do not contain the proper long fatty-acid chains that should make up the regular staple of a marine predator. A few other things about keeping pet octopi... make sure the tank is ESCAPE PROOF. These are highly intelligent animals, and I have watched mine even pick a lock to his enclosure when he was living in the refugium (never did escape; I have also heard that his species is less prone to escape). Also, they are streamlined predators, and cannot be kept with other non-sessile animals unless you are ok with them being dinner. I keep mine with a blue yellow-tailed damsel only because I first intended one to be food for the other... but so far, for 2 months the little damsel has elluded Inky!
I have since heard that damsels don't make good food for their quickness, but I've decided to keep him around because he brightens up the tank and cleans up the scraps Inky leaves behind... I guess they have a tenuous relationship where the damsel is still barely tolerated... till he may one day become "emergency food". The last thing I would note is that octos deserve special care and also very slow drip acclimitization when first introduced to a tank, as they are susceptible to death by shock.
You should also research the species of octopus you are going to get before you get it (the first link below is the best place to start), as some, like the blue-ringed octopus, are HIGHLY poisonous (the most poisonous animals in the world) and can kill humans in an instant; some grow way too large for the aquarium, and some are cold water species, so you should prepare the tank in advance. I have heard that this species is one of these easiest to keep as a pet, and I have had no problems with Inky so far.