To start, bend your arms at a 90 degree angle. Make a pumping motion from your shoulder. Make sure you're swinging them naturally like you're reaching back for something. When you swing your arms forward, be sure your wrist doesn't go any higher than you chest.
Now here's where the challenge to yours truly comes in (Coordination not being my forte!). You want to move your arms in the opposite direction of your legs. That is, you should swing your right arm forward when you take a step with your left leg.
Make sure your hands don't clench or you'll be sorry later if you're prone to joint pain (aching fingers, anyone?). Also, you'll want to keep your elbows close to your sides, so don't let them move outward as you increase your pace.
