When it comes to learning how to breed Betta fish, you should be sure you know what you're doing in order to avoid a lot of hardship and frustration.  That being said, breeding can be a rewarding process that for many grows into either a larger hobby or a small business, as many potential Betta owners would prefer to buy from breeders than from over-crowded pet stores with poor conditions.

1)  The first step to getting Bettas ready for breeding is called conditioning, and usually occurs for about 1-2 weeks prior to actually introducing the two fish to each other.  A good foot for nourishing and fattening up your breeders is any sort of live worm sold in most pet stores.  Two worms twice a day to each fish will ensure that they store of on proteins and fats necessary for a successful breeding cycle.

2)  In preparing a breeding tank you will want to have a completely clear and uncluttered tank bottom, as gravel and other common substrates can trap eggs that fall from the floating bubble nest.  Also, while the male is in the breeding tank and the nest is being built it is best to turn off any filters you may have running, instead opting for a couple of plants instead, which will also provide food and shelter for the fry.

3)  Introduction is the next step in learning how to breed your Betta fish and it is recommended that you place a female Betta in the breeding tank first to let her get used to her surroundings and then add the male when she is comfortable. 

Soon after introduction, the male will start flaring and building his bubble-nest along the top of the water, at which point you should be very careful to keep noise and light down and not disturb the two fish.

4) The actual breeding occurs when the nest is finished and both fish are ready.  This readiness is usually signified by a sort of courtship dance by both fish and may go on for a while before actual mating.  During this time the male should become less aggressive and more playful, enticing the female to come to his nest when it is ready.

5) Very important to a successful spawn of fry is the post-mating process, which will take some involvement from you.  After mating, both of the Betta fish with scoop the eggs up off the bottom of the tank and place them up in the bubble-nest.  A few moments after breeding you must remove the female from this tank as the male will chase her away aggressively and it is dangerous for her to remain, furthermore, it is now the male's job to scoop up and rescue to the falling eggs.

While this should give you a good basic run-down of Betta breeding, for the best resource on the inside secrets of professional Betta breeders and caretakers I recommend the Betta Fish Secrets guide, it has entire sections dedicated to setting up perfect breeding conditions AND you also get all of the Betta care info you need to successfully raise Betta fry after birth (see below for more info).