So you want to propagate begonias? Well, it takes some knowledge of what it takes to be successful. Begonias require a very well drained prop mix whether it be leaves, stems, pieces, etc...
Do you have a greenhouse? If not, a large plastic tub will also do but make sure it is sterile. The best prop mix is similar to:
1/4 dry peat moss
1/4 vermiculite (large type preferred)
handful of bone meal for some in initial fertilizing....
Drier climates can use more peat moss. Thoroughly soak the mix prior to sticking the cuttings. More to come.