The running mechanics are important to improve straight-ahead speed. Practice these mechanics every day! Strengthening your body (core included) will also help make you faster.
You have to train fast to get faster! This might sound simple but how many times have you seen coaches have their players run "sprints" after practice. That IS NOT speed training---that is general conditioning!
You can only run full speed when your body has recovered. That means you need adequate rest between sprints in order to run each one at full speed. About 1 minute of rest is needed for every 10 yards sprinted. So, you would need 6 minutes of rest between 60 yard sprints.
Coaches, instead of having your players run sprints after practice, make sure that they practice at full speed during practice and drills. And, a better tactic would be to run sprints before practice when your players are fresher (they would still need adequate recovery between sprints).
The same holds true for plyometric exercises such as squat jumps . These drills need to be done at full speed with adequate recovery time between sets. Drills like squat jumps help improve speed and power.