Cant find my book and havent done this with azaleas, but:

bound to be able to take cuttings cos thats the easier way to propagate most things vegetatively and azaleas have a lovely swooping habit which suggests that they root when they touch the ground. If yours does that I would help the process along by digging a hole and filling it with potting compost, then bending a stem down to reach the ground and pegging it down before covering it with compost and standing a stone on it. To help matters along I would damage the stem by partially slicing it and then bending it quite sharply whilst keeping it intact.

Finally I would take some cuttings now from a young shoot, pull the leaves off except the top 2 and then put them in a pot with half sand half compost. Stick a stick in it and put a clear plastic bag over it. Water it to begin with but then keep it reasonably dry - just mist the leaves occasionally.

Thanks so much Sarah, that's brilliant info. Off to buy some sand now!