When the male and female are ready to breed, the male will swim next to the female and display to her (flare his fins out). After a few minutes of this, the male will push his side against the female's side and they will stop for a moment and expel eggs & sperm. The male then picks up each egg and coats it in a mucous bubble and puts it in the bubble nest. When he has picked up all the eggs that were laid then, he will swim back over to the female and show off again and put his side on her side and they will expel more eggs and sperm. He picks up those eggs and puts them in the nest. They do this until the female has expelled all of her eggs. Then the male will chase the female away and look after the eggs in his bubble nest.
If the male is nice and the tank has lots of plants in, the female can sometimes be left in there. However, most males will chase the female away and if the tank is too small, the male might kill the female. So it is best to carefully remove the female after they have bred.
Once the female is out of the tank, the male guards the eggs and looks after the babies during the first few weeks of their life. Then the male can be removed and the babies can be grown up.
You need to keep a cover on the tank with the babies so the air above the water remains warm. If the baby fish take in cold air it can cause problems. Having a coverglass on the tank will keep the air warm and the babies won't be exposed to cold air.
Baby fish should be fed on infusoria and green water for the first few weeks of life and then fed newly hatched brineshrimp. There is information about culturing live foods like infusoria and green water at the following link. It is a good idea to start live food cultures well before you breed the fish so you have food available when the babies hatch.
http://www.fishforums.net/threads/back-to-basics-when-breeding-fish.448304/