If you want to learn how to run faster then what you're about to learn may challenge some of your pre-existing notiions of running and training. But that's ok because that's how you grow and improve.
Running faster boils down to a few main factors:
increasing stride length
increasing stride frequency
improving lactacte threshold and VO2 max
being able to spend more time running at your fastest possible speed
Increasing Stride Length
Stride length is biomechanical in nature. Since running speed is equal to your stride length x your stride frequency, it is necessary to improve both if you wish to run faster.
Stride length is the distance between your right and left foot as move forward in your run. If you have longer legs, naturally, your stride length would be greater than someone with shorter legs.
One of the best ways to improve the length of each stride is by stretching the muscles of your hips, specifically your hamstrings, hip flexors, glutes, and quadriceps. If these muscles are naturally short or stiff due to genetics and training, respectively, then they will lessen your range of motion, and thus limit your ability to increase your running stride.
Here is a video to give you some stretching ideas for those muscles:
Another method of improving your stride length is to run uphill. Doing so, strengthens important muscles deep into your pelvic region, especially the upper hamstrings and glutes, which are true "powerhouse" muscles for running and vital for helping reach farther and longer with each step forward.
The other helpful element of hill running is that forces you to run with running form that closely resembles sprinting. For instance, you are more likely to land on the balls of your feet (instead of your heels) and drive your knees - both very important elements of sprinting. As a result, you inherently train your body to run more like a sprinter, which will obviously help you run faster.
Improving Stride Frequency
The other part of the running speed equation, from a biomechanical stand point, is the turnover rate - or stride frequency - of strides over a given distance. If two people have the same stride length, the one who can cycle their legs quicker will be a faster runner. Stride frequency can also be viewed as RPMs (revolutions per minute). Although we don't use RPM for running, it can be helpful to think of your legs as bicycle, wherein the faster the pedals (ie. your legs) move, the faster you will move.
One technique for bettering your stride frequency is to run downhill. Although, doing this on a regular basis may not be such a good idea for the health of your knees, it can prove to be helpful in learning proper form. The neat thing about running downhill is that it forces your legs to "cycle" faster to keep up with the pull of gravity and prevent falling forward. To get the most out of this type of running, try to avoid excessively lengthening your strides and instead focus on cycling your legs quicker. To help you do so, focus on kicking your heels towards your butt after each foot strike. Doing so will help you create more angular momentum about your hips and enable your legs to move more quickly.
NOTE: Kicking your heels towards your bum should also be considered when running on a flat surface for the same reason. It's one of the best ways to get your legs moving faster.