Like the pp, I took this about 10 years ago also. One fair warning though. If they do do this, they risk catching the bug, and by that, I mean the scuba diving bug where they will want to get certified and you will have to go Caribbean and south pacific trips for years to come. Oh the horror! I know because that is what happened to me. With in the year that I took the aqua seas tour, I became certified and one of the first dives I took afterwards was back in the living seas aquarium. Since then I have done it several times. The best of both worlds, Disney and a dive trip all in one.
That being said, my review would also be dated but for lack of other reviews, here is what you can expect. All equipment is provided including a shorty wetsuit, but you must bring a bathing suit too. They have lockers, locks, towels and soap/shampoo for a shower afterwards. They take you to the top of the aquarium where there is a shallow platform where you can stand and gear up. They take you through the onstage viewing area to a central enclosed stair case. This provides one photo opportunity for a waiting family member. I'm not sure put you should also be able to get some photos from the viewing area of them in the water also. Basically what they will be doing is floating and swimming along the surface looking down(like snorkeling) while breathing through a scuba regulator and wear a vest that keeps you floating. Absolutely no experience is necessary, they will show you everything. It may seem strange for them to breath that way at first and may breath very fast but with in 5 minutes tit will be second nature to them. You can not dive down, but you can duck under, like a duck, if you want. You can go around 3/4 of the way around the donut shaped aquarium. The other part is reserved reserved for the dolphins and you are not allowed near gate separating them. The tank is about 82 degrees and 26 or so feet deep so you can clearly see all the way to the bottom. You can get close to many of the inhabitants but are not allowed to touch them or initiate contact, taunt them etc. Of course, if a turtle comes up and it wants to brush up along side of you, thats fine. Your small light weight tank has plenty of air for the experience(forget how much actual water time there is) and they have people in the water to watch and help if needed. There are a hundred or more different varieties of fish, turtles etc. including reef sharks. No need to be worried about those. They typically stay close to the bottom, are well fed, have seen hundreds of divers at their level and are not interested in bothering you.
All in all this is a great unique experience. Our tour included a behind the scenes look at the aquarium, a picture at the top of the aquarium and a t-shirt. Also, you can bring your own prescription mask if you have one, but are not allowed to take cameras in the water.
Hope this helps!