Get a barbell on your back, (weight doesn't matter too much, the purpose is to take your arms out of the movement) get on your knees, and explode to your feet.
Deadlifts and Jefferson lifts will round you out too as well as plyo's. (as stated above)
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.
I want to try out for a semi pro football team next year and want to run around a 4.6 forty. Last time I timed it I was around high 4.8, that was after not running in a while and just getting into it. I don't have a gym around me so I do plyos with what I have, park benches and picnic tables. I really want to improve my explosiveness and quickness being that my top end speed is decent.
There's some good articles by DeFranco about increasing speed and acceleration.
Olympic lifts will benefit you. So will prowler and car pushes, and sled drags, if done with correct technique.
Multiple hops in a 3 or 4' pool are a good way to increase plyo volume with minimal impact.
Top end speed really isn't as important to football success as agility and the ability to change direction, so I suggest you work on ladder, agility, and foot work drills as well.
I did a powerlifting program for month, no cardio and shaved .2 off my 40 time, my before time was 4.2 ....no big deal and increased my long jump by 5 imches yo