First, what type of speed are you looking for?
Are you a track and field athlete running 200 m? A team athlete where acceleration during the first 5-10m and change of direction is most important? Etc.
Figuring out some baseline measurements are always a good start: vertical jump, broad jump, 40 yard dash, 100 m, etc.
Improving strength, power, and SSC will all help to improve your speed.
Olympic lifts are great for building power, but they require a high level of skill. Finding a decent coach to teach you is important.
Plyometrics are a great way to build power and improve SSC; however, they are also the most ill-used and abused exercise (a la your personal trainer in box gyms). Plyo's also require a certain level of conditioning and strength, and it is very important to provide ample recovery time.
Want a really quick way to get faster? Improve your technique. You take someone with little formal running experience/direction and teach them proper acceleration position and mechanics, proper running mechanics and posture, improve footwork, etc. and you can improve 40 times in season without over stressing the body.
Br