Propagating Begonia

Stem-propagating technique
Remove a top-growth cutting or tip cutting from the plant, leaving three to four leaves. Make the cut just below the stem node (the place where the leaf and stem join). It is important to be sure there is a dormant eye or bud at this node. Remove the bottom and dip the cutting into a rooting hormone, such as Dyna Gro Root Jell.

Next, stick the cutting into a container with a rooting medium -- a peat-based potting mix, sand, or perlite -- and then thoroughly water. In the winter home environment, the pot and cutting is placed into a clear plastic bag to help increase humidity until the cutting has begun to root. The new cutting is then placed in an area that is warm (about 70 degrees) and bright, but keep it out of the hot noonday sun. Depending on the temperature, it can take several weeks for the plant to root. Once roots are established, the plant can be taken out of the bag and placed in a brighter spot that gets some direct sun light. As the cutting grows, it can be repotted and cultured into a new specimen.

Leaf-propagating technique
 Remove a mature leaf and the leaf petiole from the plant. Dip the stem at the cut into a rooting hormone, and then stick it into a container with sand or a peat-based potting mix and water. Leaf cuttings at this time can again be placed into a plastic bag, but generally it isn't necessary.

Next, place the cutting and container in an area that is warm (about 70 degrees) and bright, but keep it out of the hot noonday sun. In several weeks, the stem will root. In 8 to 12 weeks, a young plant will emerge from the base of the stem. These young plants should be allowed to grow until they are several inches in height, at which point they can be separated and repotted. Once roots are established, the plant can be moved to a brighter location with some direct sunlight.

Resources:

Byron Martin, owner of Logee's Greenhouses in Danielson, Connecticut