I've had Achilles problems for many years. When I was young, they were a problem if my mileage went over 70 or 80 miles per week for very long. Now they're an issue all the time.
Here's what I've found works for me:
Stretching is the best preventative once the inflamation dies down. Stand with your toes on stairs and lower one heel at a time slowly. Repeat 10+ times per leg.
Toe raises using relatively heavy weights (e.g., 100+ lbs) seem to lead to healing. Try one set of 15 a couple of times per week.
Cut back some on your mileage and intensity until the problem gets better. Avoid hills. Replace your shoes if the heels are worn.
Speedwork is still OK if you get a good warm-up in, but I'd avoid anything faster than mile race pace. If the Achilles still hurts after a warm-up and some stretching, skip the speedwork and try again another day.
Avoid morning work-outs. If you must run in the morning, walk for 5+ minutes first to get things a little loose.