Try this. Stand erect. Keep your head up and gaze downward as Tom Hanks says. Tighten your glutes a little so your butt doesn't stick out behind you. This also rocks the pelvis forward a little.
Next, bend both arms at the elbow. Now, move both elbows BEHIND you. Notice that you have to lean forward a little onto the ball of your foot to keep your balance. This butt-tucked, forward lean is a very good running position. If you moved one arm forward as if you were running while standing in this position, your forward lean would cause you to have to run to keep from falling.
Next, the arm swing.
The elbows should be behind you throughout most of the arm swing, going almost parallel to the ground on the back swing and pointing roughly straight down on the front swing. The hands should not come up several inches away from your chest on the front swing, but they should be close to the chest. (Note: Sprinting is different.)
The hands should not cross the body on the front swing past the midpoint of the chest.
Ideally, the hands should go back and forth in the same plane as your forward movement. However, some runners, especially women, can't move their hands in exactly the same forward plane and it doesn't seem to impair their running, so this part of the arm swing is more up to you.