Azaleas have gotten an unfair reputation for being difficult to propagate, which is not true - not for the evergreen types, at least.
Typically Azaleas are propagated by cuttings in June or July just as the current year's wood is starting to harden off. This is called semi-hardwood cuttings. But you are not limited to taking cuttings in summer. Mid winter is another good time, but at this time cuttings would be true hardwood cuttings.
Collecting the Material
Start by collecting suitable material. Cut 4-6" tips from the ends of branches with same year's growth. This wood is usually lighter than the thicker, darker, wood from previous years, although midwinter the type of wood is less critical.
A single whirl of leaves is all you need but try to select cuttings with more leaves on the stem. A "whirl" is the top cluster of 4-6 leaves arranged in a rosette shape at the tip of the stem. Some cuttings will have only one whirl but no leaves along the stem. You can use these cuttings, too, but rooting is easier if you choose cuttings with more leaves on the stem in addition to the whirl.
Preparre the Cuttings
Start by removing the lower leaves so only the top whirl remain. Small buds are located along the stem where the leaves are attached. These buds consist of meristem tissue from where roots will eventually grow.
If the leaves are very large, cut them back by 30-50%. This will limit evaporation and reduce chances of the cutting dry out. In this manner, you can also fit more cuttings into the pot or flat.
Next, cut the stem 3-5" below the top. Best result is had if you cut it at a slant. It is generally recommended to use bypass shears or a sharp knife, such as a razor blade.
If flower buds have developed, they should be removed before striking the cutting. If the flower bud is left, the cutting will try to flower in spring draining much needed energy.
You can remove the flower bud by gently folding the young small leaves apart at the tip and with your thumb and forefinger rock the bud back and forth until it comes loose. In midwinter the buds are fairly large and easy to remove.
