Getting ready to go fast involves a progression. The key to safe, and effective speed training is getting the body used to moving rapidly. This takes a little time and it involves several things happening concurrently in the body.
The CNS will become better at connecting the pathways which link the alpha motor neurons to the peripheral nerve fibers to the synapses at the neuromuscular junction. You will fire faster.
The muscles will preferentially recruit the Type IIx fast-twitch fibers (your most explosive). These atrophy in the absence of use and that's why speed training is essential for Lifetime Athletes.
Your connective tissues will develop higher integrity to effectively transfer and manage the high, rapid forces which speed moves through the body.
And there will be a coordination, rhythm, and timing in which your body learns the dance. Speed is a skill that requires use and practice to reach a high level of polish.
All that stated, preparatory training can actually be simplified into a couple of applications, each of which can be built into the training over a few weeks, or a month. That's how we do it in T2.
Exercise tempo is our first consideration. This is the cadence or timing of anything such as a squat, press, pushup, etc. At TLA, we use the 4-phase model for exercise tempo: initial phase of lift, hold or not, return phase of lift, pause or not before next rep. It's equal parts simple and effective. In many cases we start out by moving the weight (or body) just a bit more quickly in the concentric (usually anti-gravity) phase. Then we progress onto fast eccentrics and rapid reversals, often through less than full range of motion.
Explosive lifts (Olympic variants) and medicine ball throws can be worked into the routines and these can take on many forms. It's here where we pay particular attention to exercise selection, choosing the ideal moves for each person. Skill level, and injury history can and should be respected.
Next up comes plyometrics, in both extensive and intensive fashion. Extensive plyo's are of lower amplitude and can generally be done in extended fashion. Intensive plyo's are more agressive and of very high intensity.
A great example of an extensive plyo is a pogo jump or simply the act of jumping rope. This helps an athlete too be "bouncy" and it's very safe. Box jumps in which you jump up and onto a box but then step back down are also excellent.
Intensive plyo's need to be approached with caution. These are things like depth jumps in which you drop off a high(ish) box, hit the ground and explode up onto another box. These are fun and can be great for certain athletes, but the risk versus reward situation gets a bit more challenging as we age. It's always good to err a bit on the conservative side.
Using power applications with resisted locomotion is superb. This can include pushing sleds and drag (pulling) rigs.
Ultimately, we can get to the point of moving the body quickly, such as with speed ladders, agility and change of direction drills, and the like.
Progressively including a selected sequence of these exercises over 2-4 months is very effective at getting the body speed-ready and speed-tolerant. We build this into our T2 ATP and I also do that with all my coaching clients where and how that is indicated. This type of training is quite fun and extremely popular. It's all about getting big kids into playing again. Life is your playground.