Once the bettas have bred (you'll notice that the female is on the opposite side of the tank, hiding from the male or you'll see the male chasing the female away from the nest), you should take out the female. From this point on till the fry are free-swimming (usually 3-4 days @ 80 degrees Celsius), the father takes care of the eggs/fry. He usually picks up the eggs/fry that are falling out of the nest or the eggs/fry that fell to the bottom of the breeding tank. Caution: some dads could go in two different directions from here though. 1. The dad can take care of the fry as a good dad or 2. be an evil dad and eat his eggs/fry. There are many possible reasons for this, but I will not list them here. Just remember, if #2 happens, take the father out and try to artificially hatch them. I will mention these things in 'trouble shooting' in the final page of the breeding section.
There is a debate on whether or not to feed the father during the time he is tending the nest. I have tried both ways and sometimes the statements are 50/50. I think it's really the dad that will ultimately decide whether to eat the babies or not. How do I feed them? I feed the male betta enough during the condition period, where he doesn't need to eat for 3-4 days. So my answer is that I don't feed during the nest tending.
When you see most of the fry free-swimming, you can take the male out and put him back into the barrack system or his jar (clean water). Make sure to feed him (and the female; don't forget about her--she's the one that took more of the beating) his regular food to keep him healthy; breeding and tending the nest takes a lot of energy. Usually, the male will be able to breed again in about 4-5 days. The female will be able to breed in another 2 weeks.