The American Rhododendron Society is a helpful resource and has the information you seek on propagation:

Propagation of hybrid Rhododendron plants and selected cultivars of species requires a form of cloning.  These include cuttings, tissue culture, grafting, and layering. Most rhododendron and evergreen azalea cuttings root fairly easily.  Deciduous azaleas require special techniques to root.

Most rhododendrons and evergreen azaleas may be propagated from stem cuttings.  Cuttings are usually taken in the early fall from new growth that is just beginning to harden off.  Generally, softer wood roots more readily than harder wood, though the softer the wood, the more likely it is that problems will occur with fungus-related diseases.  Cuttings are taken in the morning when full of moisture.  Read more here.

Courtesy of NYBG Plant Information Service