Every breeder has their own methods of breeding bettas. The following guide is from my personal experience and I'll try to keep it as simple as possible. Breeding them isn't as challenging as most would think. Season breeders would know that the real "work" begins when the eggs hatch!
Conditioning Phase 1
The term "conditioning" is used to describe the phase where the pair is introduced to each other. In phase 1, the pair should be placed in individual tanks (as they are kept in) and exposed to each other (opaque partition removed) for a short period (10-15 mins) of time daily for a week. This allows the pair to get used to each other which minimize injuries during the breeding process.
Conditioning Phase 2
Upon completion of phase 1, prepare the breeding tank. 1 feet tank size would be optimal. Half a styrofoam cup can be used as a shelter for the bubble nest to be made by the male. Place the male into the breeding tank and the female into a smaller tank which is also placed in the breeding tank. Allow the male to build the bubble nest for 1-2 days.
Upon completion of phase 2, release the female into the breeding tank. Observe the pair for the next few days. Breeding can occur as fast as within a few hours upon releasing the female to as long as days. Fights and chasing will usually be observed during breeding. Should you notice that either the male or female is suffering from severe injury, do remove the pair and start the conditioning phase again. For pairs that suffered minor torn fins, you may continue to allow them to stay in the breeding tank.
Upon discovering eggs in the bubble nest, you will notice the male tending closely to the nest and the female would likely be hiding at a corner. At this stage, you may remove the female. The male will stay close and pick up any eggs that drop from the nest. The eggs would roughly take a day to hatch. After the fry has emerged, allow the male to take care of them till they are able to swim freely, which usually takes a day. The fry can be fed daphnia or baby brine shrimp till they are bigger to take tubifex worms or pellets.