I’m in the middle of getting trained as a volunteer at the Denver Downtown Aquarium (DTAQ). The vast majority of divers you see in there cleaning and feeding the fish are volunteers (although most of the staff Aquarists are also certified and have been trained).
Before they’d even speak to me I had to be Rescue certified and have a minimum of 50 dives in the wild. After an interview with the volunteer coordinator, followed by a drug test, I had to pass a DM-level swim test (tread water for 10 minutes (or 2 w/o hands), uw swim 25 yards on one breath, 300 yards in less than 15 minutes w/o any gear). Next was the scuba skills test: mask and regulator recovery, uw swim w/o mask, bouyancy control; I seem to remember there were a couple of other skills but I can recall them off-hand.
Anyhow, after passing all of that I have to do several dives in each tank, with a specified instructor, to learn the protocols of cleaning and feeding in each exhibit, including equipment set-up and breakdown, radio communications, and emergency procedures (which is mainly letting everyone know your buddy is in trouble via the radio, then helping to extract them from the exhibit.
As for equipment - they provide tanks (including fills), weights, belts, BCD’s (including integrated weight pockets), regulators, and fins. There are a few wetsuits available, and a drysuit for the cold tanks (if you fit it and are qualified); we’re expected to provide our own masks, wetsuits, gloves, booties, and hoods even for the warm tanks (very important - the fish have learned that ears and hair are fun to nibble on!).
As for compensation, we get free admission for ourselves all year (of course), a few guest passes a year, and they throw us a nice thank-you dinner once a year.