Since you are asking specifically about increasing your 100m speed, I am going to assume you want to focus exclusively on improving your sprint event speed. (I make this distinction because increasing your distance race times is a very different process and strategy than increasing track or sprint event times.) However, training for both distance and sprint events start out virtually the same. You need to focus on increasing stamina and endurance. Slowly increase the milage you are logging on your long runs each week.
Next, focus on other speed workouts during your training plan. Throw in tempo runs and various speed drills to work on quickening your leg turn over. One way to do this efficiently and effectively is by taking to the treadmill and setting the pace yourself so you know what it feels like to run at that pace. Throw in 100m runs throughout the week too, so that you get your body and your legs used to the distance. Knowing what it feels like to give 100 percent of your energy into such a short distance will make actually doing so during your race easier.
Next is to focus on technique and form. Your posture should be good, as this will translate to a much more efficient run. Keep your head down, core tight and back straight, and focus your eyes the entire time on the finish line, 100 meters out in front of you. And use your arms! They should be stiff like knives, and your elbows locked into a 90 degree angle. Pumping your arms fast typically helps signal your brain to do the same for your legs.
Strength training in the gym will also make you a better and faster sprinter. You will build up the muscles you need to run your fastest. Be sure to focus on legs (squats, lunges, and dead lifts will specifically target your hamstrings, glutes, and quads) and core (to benefit your posture). Finally, be sure to take care of yourself. Getting plenty of rest and having proper nutrition will make all the difference in your running performance.