Propagating Begonia rex has a good success rate and is quite easy for any level of plant aficionado.
Pick off a mature leaf and put it in a small bottle or glass of water up to where the leaf joins the stem. Roots should form over 4 weeks.
By leaf cutting:
Cut off a mature leaf. With a sharp and sterile pair of scissors (wipe with alcohol) cut around the stem as shown in the diagram. That's cutting number one. Then with the remainder of the leaf turn it over and look at the big leaf veins - you want to cut a wedge cutting that has the vein in the middle (this bit is important). You should get another 5-6 wedge-shaped cuttings. Begonias are the only plant you can grow from cuttings like this.
Prepare a tray of propagation potting mix (usually a finer version of potting mix), dip in clonex gel and poke a hole or a slit into the soil with a dibbler or knife and poke the cutting in. Done! Water gently with a soft shower head, and put on a heat bed with a cover over it for humidity. You get a lot more cuttings this way than by water propagation over the same amount of time.
Pro tip: Get a small spray bottle or re-purpose an empty spray bottle from your recycling. Dilute some auxinone (a liquid rooting hormone) in the appropriate ratio for your bottle and spray on the cuttings every couple of days.
Where to buy:
Rural supply shops, hydroponic supply shops and Bunnings have most of what you will need. Most can also be brought online.
Heat bed: Bunnings $50, Online $40+
Auxinone: Fernland $40 for 500ml (share with some friends)
Propagation box: Bunnings $10
And you can get the begonia from us!