With livebearers, there is really very little to breeding. Most of them just need some gadget to ensure they won’t eat their fry. Just keep males and females together, at a ratio of at least 2 females for every male, (having too many males can oversex the female) and let them go at it.
Soon, some or all of the females will swell up real big. These are pregnant. Now comes the tricky part: you must give the fry (babies) a place to escape to, lest they be eaten by their parents. Breeding traps are commonly used, but the female must be housed in there when you think she might give birth, which is essentially guesswork, and you don’t want the females to be in there too long. You also don’t want to wait to long or she will drop outside of the trap.
A better (in my opinion) alternative is to provide places inside the tank for fry to hide. Java moss, while hard to find, is best. It proves a large network for fry to hide in. (provided you can grow it large enough) Probably the simplest method is using marbles as a substrate. Since livebearer babies are full of yolk at birth, they sink. If they sink down into the gaps in the marbles, they will be safe from thier parents. Try to use round marbles to prevent small crevices from forming where fry can get stuck.
You can then feed the fry with baby brine shrimp, daphnia, microworms, or fry powder. Many of these foods can be purchased at your average fish stores.