Wow I'm very happy for you! I love new betta owners who are ecstatic about their fish!
Healthy Betta Diseases/Cures: http://www.healthybetta.com/fish-ill...re-information
The main key with bettas is making sure you have a heated, filtered tank, test strips (unless you can afford the 30$ kit) and adequate room for them to live. (2-3 gallons each is best for them).
You probably didn't have your tank go through a 4-6 week cycle, so when you clean it you'll want to do full water changes based on when your ammonia levels get high which is what the test strips or ammonia kit is for. (their poop and pee creates ammonia)
My guess is your tank is divided?