It's not as simple as dominant and recessive when you're concerned about how various traits will inherit (ie. 'what will I get if I cross...')
Firstly the basics, which I'm pretty sure you know but I'll go over it anyway.
The code for a particular trait is made up of two alleles... think of alleles as spots where genes can go. Any betta will have two genes for each trait. A dominant gene is written as a capital letter (D) and a recessive gene as a lowercase letter (d). A betta with genetic code DD is homozygous for the dominant trait, and obviously will show that trait. A betta with genetic code dd is homozygous for the recessive trait and will show the recessive. A betta that is Dd is said to be heterozygous, or [dominant] split for [recessive]. So a red betta that is split for cambodian carries one copy of the red gene and one copy of the cambodian gene. It will be red, and there is no sign that it's carrying the cambodian gene because the gene is masked and not displayed. (This is a good reason to buy from breeders - knowing the genetic history of the fish.) But it can still pass this gene on, so if you breed it to a cambodian or another fish that is split for cambodian, you might get some cambodians back. You can predict these outcomes using punnet squares. I can't demonstrate them on here with the formatting of this post so if you don't know what they are (I'm pretty sure you do though) google it.
Now if it would stay like that, genetics would be easy, but it doesn't. The big one is codominance - when you have two genes that occupy the same allele set, but they are equally dominant (let's call them D and X this time.) So obviously DD and XX would result in fish displaying traits D and X respectively. But DX would result in a mixture. An example of this is the complicated combtail/crowntail genetics which I don't fully understand but I believe it is codominance that causes it - if you breed a crowntail with anything else, you end up with a fringe-finned betta (a combtail) - slight ray extensions over the top of whatever tailtype you crossed with the crowntail.
On top of this, there are a lot of traits that are controlled by more than one gene - for example, there is not a 'halfmoon gene'. For a fish to be halfmoon you need the appropriate genes for ray straightness, ray splitting (number of branches), degree of webbing between rays, length of fins, and the 180 degree spread. If one of these genes is missing you don't get a halfmoon. I believe there are also colours like this and I don't fully understand it.
www.bettas4all.nl - helpful links in the genetics section. They go over a lot of what is dominant, what's recessive, and as much as is known about how traits that aren't this straightforward inherit.