Improving your running speed, pace, and race time comes down to a very individualized training program and structure that is tailored to your individual needs, and which involves a variety of running workouts. It is first important to understand that getting faster as a runner is not always first and foremost about incorporating more speed work and exercises into your regimen - though it often does not HURT your chances of getting faster. In reality, if you want to increase your speed, most runners find that it takes a very systemized combination of sprint work, tempo drills, long runs, and even appropriate rest days and time spent in the gym building muscles and strength.
As far as speed drills in particular are concerned, though, there are a number of fairly simple drills, exercises, and techniques you can employ. The first thing to focus on involves technique; mainly, it is imperative for you to have good running form. Good running form translates to much more efficient running and subsequently, a faster pace. In short, this includes a relaxed upper body that is still held tall with your eyes focused up and out, and a foot strike that lands in-line with your hips while you keep your arms swinging at your sides (NOT chicken arms swinging laterally) at a 90 degree angle.
While it might not be your favorite way to train (heck, you either love it or hate it - there's really no in between), taking to the treadmill can pay dividends in shaving off race time. That is because it helps get you accustomed to a certain pace, so your leg turn over is "used" to functioning and moving that quickly. Just work your way up to your goal pace by manually punching in the numbers. And then, after the treadmill comes the track. Take to the track to incorporate true sprint drills. Start out with striders, which are a form of sprint in which runners focus on striding their legs out, opening their hips, and incorporating their hamstrings. Then get more intense with timed sprints of different distances - anywhere from 50 to 400 meter sprints will really help your body figure out what it means and feels like to run fast.