I've read a fair bit up on betta genetics, but me trying to write up a post on them here would be ridiculously long and drawn out.
....besides, there's other pages that have already explained it nicely with pictures and everything else that I probably couldn't fit in a post, and I'm lazy this morning xD
Start out with that one, it's a nice, simple easy introduction to genetics for those who have maybe been out of their bio-classes for a few years and need a refresher course on punnett's squares.
And from there go on to a myriad of other sites on the topic.
BETTAS by Jim Sonnier/genetics
^There's several pages on it there, remember to click through 'em.
^Probably one of the more detailed betta genetics pages out there.
Betta Splendens - Half Moon, Double Tail, Crown Tail Bettas - Genetics Study
If you've got a lot of time on your hands, you're bored, or you're deathly curious like I am, this is a fun site. There are literally hundreds of articles here on bettas, on pretty much every thing and anything relating to bettas. Hopefully the category section I linked up is the one that brings up genetic related articles.