Azaleas are not hard to propagate from cuttings... but they have to be relatively small. It is difficult to get cuttings to throw roots if they are 3 years old or older (at the cut site). So you want to make sure the cutting is this year's growth (green) or last year's growth (brown but still flexible). Once they get thick and inflexible, it isn't as easy to propagate via cuttings.
Otherwise the best time of year is during the active growth season - spring to early summer.