Guppies are known for being the easiest aquarium fish to spawn. Females give live birth frequently, to well-developed offspring. The only hitch in guppy breeding is that guppies, like most fish, have no reservations about eating their young. There are several ways to prevent this.
One way to give your baby guppies or "fry" a fighting chance is to densely plant your aquarium. It does not matter if you use live or artificial plants, as long as the fry have plenty of hiding places. Occasional losses will still occur, but you will start to see baby guppies surviving to adulthood, sometimes to the point of overrunning your tank.
Another method of saving guppy fry is the spawning box. Pet shops sell clear boxes that will either clip on or float in your aquarium. They have a mesh portion, with holes that baby guppies can use to escape. You put the mother in the top portion of the box, and the fry swim to safety in the lower portion of the box. Depending on the design, you can either raise them in the box or use it to move them to their own tank.
The Spawning Tank
In this method, you move the pregnant guppy into its own spawning tank. Once they have their babies, you move the mother back to the main tank and raise the guppy fry in the spawning tank. You will still want plenty of aquarium plants to protect the fry as the mother spawns. You should also use a cup to transfer the mother, rather than a net, since nets can stress out the mother guppy and harm her or the fry.
When to Mix
You can bring guppies back into the main tank when they are large enough that their parents (or any other fish in the tank) physically cannot fit them in their mouths. This size will vary greatly among individual fish. Guppies range in size somewhat, so there is no one size that will work every time. If you wait until the fry are substantially larger than their parents' mouths, you have a good chance of cohabitation.