Your legs are obviously the most important part of the body in running. They do the work, specifically the hamstrings (back of the thigh) and calves, although the quadriceps (front of the thigh) are called into action whenever a runner needs to run up a hill. Still, unless you are perpetually going up, it's the hamstrings in particular that do the lion's share. New runners generally develop their hamstring muscles at a faster rate than their quads, which unfortunately can create a muscle imbalance, leading to improper tracking of the tendons that surround the kneecap. Patellar Tendonitis and Iliotibial Band Syndrome are common for those newcomers, but can be avoided or minimized simply by following a set schedule, and not ramping up the mileage too quickly. Proper running shoes that are suited to the individual runner are a must, as well.
As I stated earlier, there is nothing in front of you that is going to help you go faster. This is especially true with the legs. Many runners overstride, and it's almost always caused by heel striking. Your feet should be landing directly under your centre of gravity. This is your hips. In fact, if you aren't looking directly down, you should not be able to see your feet at all. The degree of knee lift is proportional to two things - how fast you are going, and degree of incline. If you are not running up a hill, and you are moving along at a comfortable pace, there should not be much knee lift at all. Lifting the knee is lifting a weight. Don't do it any more than is needed.
A difficult part of the leg movement cycle to master is when the foot should be hitting the ground in relation to where it is in it's cycle of motion. As I mentioned, many runners will overstride, making hard contact before the weight of the body can catch up, and this results in a perpetual braking action. You do not want to be landing on your heels. The heels should make contact with the ground, but only a split second after the forefoot. The forefoot (or ball of foot) should take the weight of your initial strike. If you overstride and heel strike, the strike of the foot itself momentarily stops forward motion, which the runner must fight through over and over again! No one wants this. Also, heel strikers are landing ahead of their center of gravity.
Although it's hard to master, try to already have the foot motion just barely (but already) on it's way back just before it strikes. Don't strike at the end of your forward motion, then move back. I would argue that this one thing is perhaps the single biggest difference between an average runner and a good one. This is very subtle, but an extreme way of looking at it is imagining you are log-rolling. If you were trying to keep your balance while running in place on a log that is rolling in the water, you would certainly follow this principle! Another principle you would follow while trying not to fall in the water is a short stride rate, since there's a small area under you in which it is possible to place the foot. Remarkably, the log-rolling analogy applies here as well, since the place where the log would be is exactly under your centre of gravity.
I will expand upon this, as it's very important: Think of riding a bike - your foot is already on the way backwards when it is at the bottom of it's cycle, which is the same moment as the footstrike in running. Work on this all the time, and you will get much faster, and reduce impact dramatically.