You can start by reading this:
http://www.reefsmagazine.com/forum/reefs-magazine/151543-macro-photography-coral-reef-aquariums.html
I can take those pictures with my galaxy note II. If you want to get more in depth then a macro lens will help.
I have a canon t3i with a canon 100mm macro lens IS.
An Iphone5 can do it. As far as glass goes the L is an amazing macro lens but you pay for it. I'm currently saving to add it to my L collection. The EF 100 is a very nice lens also.
These are from my Iphone5. No post processing.
What equipment should I get (camera/lens/flash etc) and any tips on technique or setup? I pm'd the photographer on another forum but have yet to hear back.
Canon or Nikon is up to you. You can pick up a Nikon D3100 or a Canon T2i. The close up pics are shot with Macro lens. (meaning they can be taken close up where a camera phone or regular lens requires a greater distance). Buy the camera body though and avoid the kit lenses, they are trash. Get a 60mm Macro lens or perhaps a 100mm macro lens f/1.4, f/1.8 or f/2.8. You will be very happy with the results.