Condition the male and female for some time (at least 3 weeks) each in their own tank. Have a third tank large enough to house potentially 300+ fry until they need to be separated due to aggression. There should be no gravel in the spawning tank so the male can easily get eggs that fall from the surface. The water level should be around 6 inches so the male doesn't get tired from going up and down constantly for days on end. There should be floating plants in the water and something cup-like floating at the surface for the male to build his nest in. Some use a styrofoam cup cut in half. You should have cultures ready for feeding the fry that will come in as little as 24 hours.
Once both bettas are conditioned, the male is put in the spawning tank so he can start building his nest. The next day, you can put the female in a glass tube placed vertically in the water so she has access to the surface of the water. After they are showing interest in each other that doesn't look aggressive, you can try to release the female. The entire breeding should be supervised so you can prevent any serious damage to either betta. When they are finished, you remove the female back to her own tank and allow the male to tend to his nest and eggs.
Keep the top of the tank sealed when you aren't doing water changes or feeding. Some people use clear plastic wrap and a rubber band. Warm, humid air is essential for the fry to develop their labyrinth organ. Some males have a tendency to eat their eggs and fry, so observe and remove the male to his tank if he does this. Otherwise, you leave him in until the fry are free swimming. Once they are free swimming, you remove the male to his tank and you can feed the fry. At first the fry live off their egg sacks, but in a couple of days it will be used up and you will need to feed the fry every 4 hours or so. You will have to do frequent water changes. As the fry grow and start to show aggression, they will need to be separated into their own tank.
There are SO many details that I didn't go into because I'd be writing a book here... also, it's been written out all over the place in this forum. If you do a search, it will turn them up. Check out the FAQ in the pinned section, too.