This is the shortest page on my site because all it has are links to the two best sites for learning about the genetics of betta colors. They say everything I could say, do it more clearly, and have a host of pictures to exemplify genetic traits.
I recommend starting with Betta Genetics at: http://www.geocities.com/dynarb/genetics.html. This is a page on the Betta Bunnies site, maintained by Dynarb and he does an excellent job of explaining the nomenclature and mathematics of genetics.
Once you've read through that site, I recommend visiting http://vanriel.myadsl.nl/BT-AABcolorgenetics.htm. Here you will get a detailed and easy to follow guide to all the myriad colors bettas exhibit, how they are created, and the genes responsible for each.
(Click on Bettas to return to the main betta page or on main site to browse 70 topics ranging from exotic kaleidoscope designs to the strange world of lucid dreaming.)