For outdoor plants, the ideal time to take the cuttings is 6 weeks after leaf out, though with azaleas your cue will have to be from other plants since they don't lose their leaves in winter.
So, essentially firmed up new growth. These are softwood cuttings and are the easiest to root and much like rooting cannabis I suspect.
The later you go into the season the more it turns from softwood to semi-hardwood and then hardwood which are actually better taken after the plants go dormant in the late fall after the first killing frost. For those, you plant basically sticks, leave them outside and the root nubs callous over and then new roots form the following spring as the weather warms.
Also, except for the hardwood versions, rooting powder really helps increase your percentage successful "stick" rate.