Running properly is very important and there are a lot of things to consider. It really isn't just a matter of throwing one foot in front of the other and swinging your arms. Bad running techniques can lead to a lot of problems in the knee and ankle joints, as well as back problems and poor posture.
You'll want to start upright, not slumped, or looking down, even though it is tempting to look down to check the ground in front of you. Imagine there is a string on the crown of your head pulling you upright and this should keep your head up and your back straight.
When you stride forward do not over extend and avoid placing your heel down in front of your knee, as this is in front of your centre of gravity and creates a jolt, or braking effect and also puts extra pressure on the knee joint. Land lightly with the foot directly under the knee and propel yourself forward, with the foot making minimum time in contact with the ground.
Your arms also play a big part here; they assist your balance and help with the rhythm of your running. Make sure your shoulders are relaxed, not hunched up, and arms should be bent about 90 degrees. Allow them to swing naturally from the shoulder, as your left foot steps out, your right arm should swing forward.
Your breathing should be rhythmic to your stride pattern, although it may take a few minutes to get into a good rhythm and as you speed up or slow down you'll have to adjust accordingly. Try to breathe in through your nose and exhale through your mouth.
An alternative to normal running is barefoot running, this isn't literally running barefoot, but you can now buy running shoes that give minimum support under the heel to make you run on your forefoot. Most running shoes have big cushioned heel blocks, which lead us to slam our heels down first, trusting the heel block to absorb the impact and spring us forward. However, looking back, man has been running longer than trainers have been around and before trainers came along you couldn't plant your heels down first, so the running style was to land on the forefoot and lightly spring forward, the heel making barely any contact with the ground. Some African long distance runners and athletes across the world have always used this technique and to very good effect.
Be warned though, if you plan to try barefoot running keep the distance short to start off with. The ankles and calves are working much harder here and will need time to adjust to this new style, but people have noticed less knee and back problems with this technique, as the feet act as a great shock absorber, reducing the impact on the knees.
Using an old pair of trainers is also a big NO, trainers that aren't designed for running, or are very old, won't give you the support you need and can lead to ankle and knee injuries and the dreaded shin splints!! Some specialist running shops can work out how your foot hits the ground as you run and recommend the correct running shoes for you. If you're interested in trying barefoot running Vibram Fivefingers offer a wide range of shoes for the barefoot style running.