Increasing your running speed starts with dedication to a training plan. Even if it's just one that you come up with on your own, the only way you can increase speed is if you run and train consistently enough to get into good enough shape to start focusing on quicker speed. Ultimately, speed comes from a faster leg turn over, and faster leg turn overs come as a result of getting into shape. Also, having good form is crucial to knocking off minutes off your run time. Having and maintaining good form, too, takes some effort and practice. One tip for improving your form is to incorporate ab work into your training. Speaking of strength training, lifting weights can really benefit your running speed as well. Stronger, leaner muscles translates to stronger running, and stronger running leads to faster running.
Once you've established a consistent running routine, begin incorporating other types of workouts, such as speed workouts focusing on bursts of increased speed for shorter distances, and hill repeat workouts. It might also benefit you to add some treadmill running into your routine because the treadmill allows you to actually set your goal pace on the "speed" setting. Therefore, the treadmill belt will rotate at the speed you have to turn your legs over in order to achieve your goal time. This will help you get a physical and mental understanding of what it will feel like to achieve your goal time, and how much work you need to do before you can get there.
Finally, increasing speed isn't just about what you do on the roads or trails, but it's also about what you do outside of running. Be sure to stretch! Increasing your speed and increasing your leg turnover is all fun-and-games until you pull a hamstring. Also, focus on nutrition. Make sure you're getting in high quality sources of carbohydrates (whole grains and whole wheat, instead of white starches), lean proteins, good fats like omega-3's and monounsaturated fats, and plenty of water. Moderate amounts of caffeine are good too, for making your brain and muscles more alert!