In Nha Trang the reefs are shallow so scuba diving and snorkeling takes place at the same sites.

There are only two dive centres that I would really recommend in Nha Trang. Sailing Club Divers/Octopus Diving, run by Simon White, and Rainbow Divers, run by Jeremy Stein. They both offer a more professional service, have their own dedicated boats and will rent you well maintained diving equipment. Incidentally, as far as I know these are the only companies that include proper insurance in their prices.

Below are descriptions of the sites that I have dived, most of them many times, and the different marine life you can expect to see there. There are other sites like Goat Rock and Electric Nose but for various reasons the dive operators don't tend to travel there so if you're scuba diving in Vietnam the chances are you'll be at one of the sites listed below.

Make sure you choose a reputable operator with clean air fills, well trained staff and a proper set of safety equipment including, of course, oxygen. It's worth asking about these things as there are lots of dive operators in Nha Trang, some good and some not so good. For more information look at the dive shops page.
There is a recompression chamber and a hospital in Nha Trang.