1) Early Strengthening and Explosive ProgressionsOne big mistake that speed athletes make is training slow and heavy year-round. I agree that heavy strength training is vital to developing an early foundation, however, that type of training will only go so far. You may have heard the team "Train slow, compete slow", and it certainly holds true. You should absolutely do slower strength training in the early off-season of your sport, but if you don't transition your training towards more explosive plyometric and sprinting-specific training as you get closer to your competition, then you won't be ready to show up and perform.
Whether you have one main sport season during the year or several shorter once spaced throughout, save the majority of the heavy lifts for the earlier period of training. As you progress and get closer and closer to your competitive season, you need to start adding more explosive exercises such as Olympic lifting, box jumping, and actual sprint training to the routine.
2) Target the Glutes and Mind the HamstringsThe limbs amplify movement. They don't generate it. Therefore, like with long-distance running, the power generation is done by the glutes and assisted by the rest of the leg muscles down the chain.
Take the time to specifically target your glutes during training, through the slow-strength training as well as the plyometric training that we just mentioned above.
Also remember, however, that you do need to take very good care of those hamstrings as well. Being so prone to injury during exertion, preventative conditioning is vital. A balance between the strength to help and propel your body as well as the flexibility for stride-length and prevention of overstretch injuries will be crucial. Eccentric hamstring curls will be handy for protecting you from tendon strains. Heavier lower-chain exercises such as deadlifts will further the progress by training those muscles to be able to contract from lengthened positions.
3) Spend Time on One LegAgain, like with jogging, sprinting has you spending time on one leg at a time only. Both feet are never in contact with the ground at time. It seems like a minuscule amount of time, but you need to train your body to stabilize the side-to-side shift of the load it's bearing.
Single-legged deadlifts, pistol squats, one-legged glute bridges, they're all handy. As long as you can train your muscles to fire in proper sequence, one side at a time. For those in the gym who only ever do frontal plane exercises on both feet, there's a significant difference in how effectively they're able to coordinate proper balance during activity.
4) Proper MobilizationBeing mindful that aggressive mobility drills are not the magic bullet for performance, you will need adequate mobility in order to maximize your running efficiency.
Having poor hip mobility is going to be an obvious hindrance. Whether it's due to poor flexibility, capsular restrictions, or lack of muscular strength, adequate range of motion is a necessity if your stride length is going to be at all effective.
The other main area that I often see being a problem due to mobility restrictions is, surprisingly, the shoulders. If your shoulders are restricted and flexion/extension doesn't occur smoothly, then the tendency is to compensate for the lack of arm swing with torso rotation. If you ever see people running who aren't so much using their arms but rather just rotating back and forth at their chest, this is what I'm talking about. This makes for poor momentum and propulsion and is also a waste of muscular energy.
If you have these restrictions, does this mean you should be aggressively tractioning your joints with bands to try and increase range? Please please please no. It's so unnecessary to mobilize like an overeager Youtube Crossfitter if you're doing proper, conservative exercises that your body will more-willingly adapt to.
5) Remember Your CoreAs always, we bring it around back to the core.
I remember the very first time that I did hill sprints as a teenager. The sorest parts of my body the next day were, understandably, my calves, but also, surprisingly, my obliques.
Remember that you're generating an enormous amount of force when sprinting at maximum capacity. Because of this, your trunk is required to do everything it can to resist torque and deformation that the limbs are causing.
For sprinting, however, it's going to take a little more than just planks and side-planks to effectively condition the core. Since sprinting requires such high amounts of plyometric activity, the core needs to be trained specifically against those types of movements. Essentially, we need to turn core exercise into a type of plyometric exercise of it's own.
6) Arms, Bro.This is an often-overlooked area for runners, and many will skip arm day because, well, you don't exactly run on your hands. (Most of us don't, anyway.)
However, especially in my young runners that I coach, arm strength is lacking to a fault. When you sprint, your arms need to be driving back and forth to counter the movements at the leg. So often, I see sprinters who do not have the explosive tricep activity in order to drive their arms back with enough force. Because of this, the arms become unable to move with enough force to provide momentum to the run and can also slow down the entire stride rhythm due to not being able to keep up with motion at the legs.
The solution, fortunately, is simple. You don't need to adding three tri-and-bi days to your workout routine, but you should have a regular upper body workout with both strength and plyo work itself, just like you do for the lower body. Once you can push-press a significant amount of weight overhead with proper form, then you'll be able to drive the arms effectively when running.
Sprinting is a highly-demanding and technical skill; therefore, training for it is as well. Simply walking onto the field and running as fast as you can will, unfortunately, not promote the improvements that you're looking for. It requires both the on-field training as well as a specific and targeted routine in the gym. And like anything, practice makes perfect.