I haven't tried this before. Begonias are supposedly quite easy to root from leaf cuttings, so here goes.
I took a leaf from a white begonia (not sure what kind) and made some cuts along the veins on the underside of the leaf with a sterile blade.
I then pinned the leaf (cut side down) onto a pot of moistened 50/50 perlite/potting soil mix and sealed it into a ziploc bag.
If all goes as it should, roots should form at the cuts with new little plantlets, and the old leaf should just decay away. Sounds too simple to be true. We'll see...