Propagation depends on the type of rhododendron.
Deciduous Azalea - Softwood nodal (cut just below a node) stem tip cuttings are used when the new growth is only 1-2" long. Use a rooting hormone. Shade cuttings as they are susceptible to scorch. Keep cuttings under mist. Take 8-10 weeks for root development.
Evergreen Azalea %26amp; Dwarf Rhododendron - use nodal (cut just below a node) greenwood cuttings. These cuttings should be slightly woody at the base and are taken just as new growth is beginning to firm.
Evergreen, large flowered Hybrids - use semi-ripe nodal (cut just below a node) cuttings. These are typically taken mid-summer. Select a vigorous shoot. Remove the tips and cut the large leaves to 1/2 their normal size. Wound the cutting and apply a rooting hormone. Use bottom heat. 10-15 weeks to produce roots.
You can also hand pollinate %26amp; collect the seeds. Sow seeds on to an ericaceous soil mix. Do not let seeds dry; use mist. Again, bottom heat helps germination success.
Layering can be used to propagate the large flowered evergreen Rhododendron %26amp; deciduous Azaleas. It is not a recommended propagation technique for the dwarf Rhododendron species nor the evergreen Azaleas.
How to start another rhododendron from an existing plant?
Gram used to weigh down one of the lower branches with a pile of dirt and water it a lot. It would start rooting, then you could cut it from the main plant and dig it up and move it.