Congratulations. The A620 is a good camera and once you learn to use it you'll be very happy with the photos it will deliver. I have an A620 with a Canon housing and a YS-110 strobe and am very happy with it.
Advice?
1. Go straight into manual mode and don't look back.
2. Invest in rechargable batteries and a charger.
3. Go out and take lots and lots of pictures while experiment along the way.
4. Leave the lens zoomed out. Get as close as you can to your subject, then get closer if at all possible.
5. If you do have to use the zoom, optical zoom only, never use the digital zoom.
6. If you don't have an external flash yet then save your pennies for one. It will be well worth it. Don't try to go the cheap route either. You'll just end up regretting it and spending more money in the long run. A good flash is probably going to cost you more than the camera and housing combined. Just keep in mind that if you buy a good flash it will move with you to your next camera even if that's several years down the road.
I learned a technique at one of the mini-seminars at Sea Rovers that said to think of every photo as being two exposures. The first one is the background where the flash will have no effect. Adjust the shutter and aperture so that you get the exposure you want for the background and then adjust the flash power to get the exposure you want on the subject within the near field.
I've still got a long way to go but here's what I've been able to do with the A620 over the past year.
All of the photos in this gallery were taken with the A620 and a rented Sea & Sea YS25A external strobe. They were taken in Bonaire, NA and are a good example of blue water performance and what a total amateur can do with this camera in good conditions.
http://s91.photobucket.com/albums/k310/Dragon2115/Diving/Bonaire%2010_2006/?start=all
The photos in these galleries were taken the built-in strobe using the diffuser that comes with the housing. They were taken this summer just off of Beverly, MA. You can see that getting the exposure right when there's a tank in the photo can be difficult. You can also see a lot of back scatter as well.
http://s91.photobucket.com/albums/k310/Dragon2115/Diving/Clowntown%2004Jul2007/
Disregard the first two out of focus shots in this next gallery. My buddy didn't know how to half pull the trigger so the camera would focus first.
http://s91.photobucket.com/albums/k310/Dragon2115/Diving/Clowntown%2014Jul2007/
The photos in this last gallery were taken last month on a seal dive in the Isles of Shoals off of Portmouth, NH. Again the A620 but this time with a Sea & Sea YS-110 strobe. There was a lot of debris in the water as you can see but still managed to get some decent shots even at a distance.
http://s91.photobucket.com/albums/k310/Dragon2115/Diving/Seal%20Dive%2025Aug2007/?start=all