I was wondering, when it shows two different genes, that means that it can pass those ones down, correct? It'd be like they are a carrier, just the gene that is dominant in them is the other? If not, then can someone explain how it works to me?

Timain has a wonderful guide for new people that includes an extensive section on genetics. http://beastkeeper.com/thread/5218

There are dominant (green) and recessive genes (grey), you are correct. The genes shown are the only ones that can be passed on. Except in extreme cases of inbreeding(? Anyone know the new rules) the genes there are what is passed on- so it isn't too hard to predict genes.

Please let me know if you still have questions!! :)