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The classic approach to building speed is running intervals. How many at what distance would vary with the event you're aiming at. The longer the distance you plan to race, the longer the distance you'd repeat during your interval workouts.
Intervals are typically run at distances shorter than those at which you race, and at a pace faster than your race pace. Between repetitions, you would jog a set distance or amount of time - usually not long enough for full recovery.
Running hills is another good way to build speed. Hill workouts are similar to interval workouts, except of course you're running uphill repeats.
For runners who compete at longer distances, "fartlek" (from a Swedish term meaning "speed play") can be a nice break from running long interval workouts on the track. Fartlek can be as informal as varying your running speed between telephone poles while running on the road.
Finally, some runners find that adding weight lifting to their training program helps improve speed. This is especially true for those racing at relatively shorter distances.