Step 1: Running form and posture
You should have a relaxed, upright stance. Your back should be straight, head up and your shoulders should be relaxed and not up around your ears. Don't lean forward this puts too much weight on your legs leading to injury.
Arm swing helps keep rhythm and propels for forward. Your shoulders should be loose, arms close to your body, and up between your waist and chest. (They should not swing across your body -left to right). Hands should be cupped loosely, don't make a fist, this creates tension and wastes energy. Also don't carry things, like water bottles, MP3 players etc. this detracts from proper arm swinging.
Your arms should swing up and down bending at the elbow, less movement forward and back from your shoulders. Your arm swing should be synchronized with the opposite leg (left arm up right knee up).
Beginner and intermediate runners have a hell-ball( of foot) foot strike. Meaning you land on your heel roll forward and push off from the ball of your foot. Since there is a lot of extra padding on the heel of running shoes this makes sense. However some elite runners land on the midfoot or forefoot then heel then pushing off again from the forefoot. This creates a faster foot strike, hence faster stride frequency.
To maintain proper form with regards to your stride; the lead foot should stretch forward, swing down and make contact with the ground under your hip(your centre of gravity). If it is too far forward (overstriding) it could lead to injury.
Stride length and frequency
These are two major factors you can change to increase your running speed. Stride length can be increased by lifting your leg higher and pushing off harder with your rear foot. There are a number of training exercises you can do to increases stride frequency, these will be detailed in the next step.