In order to create an improvement in explosive strength, you need to improve your central nervous system's ability to recruit your fast-twitch fibers for a powerful movement as quickly as possible. To accomplish this, you should lift 4-6 days in a row. On day 1, perform a pull movement, a push movement and a leg-only movement (some sort of squat). Day 2, perform a leg/upper body movement (cleans, deadlifts, etc.) and a press. Day 3, go back to pull/press/leg. Day 4 will be same as Day 2, but do an upper/lower move and a pull and keep rotating this way for 4-6 days straight, then take a couple days off. Perform slight variations on the pulls, presses and leg-only moves so that you end up with several different but similar moves for each movement. All the moves should be compound movements which force you to recruit a larger amount of muscles and therefore more motor units.
Perform each movement either explosively with 40-60% of your 1rm or maximally with 85-90% of your 1rm. Perform 6-8 sets with short rests between each one. Do not stretch between sets as this downregulates your central nervous system and compromises your ability to effectively exert maximum force. When doing explosive movements, do 3-5 reps (never more than 25 total reps per exercise) and do 1-2 reps when lifting maximally. At the end of the week, you should be doing about 2/3 of your movements for each body part maximally and 1/3 of your movements explosively.
What this accomplishes is it forces you to become better at exerting maximum force output for a wide variety of complex, athletic movements with heavy resistance. This will naturally improve your ability to move quickly AND powerfully during sports-related actions. Since the overall volume of reps and sets will not be high enough to create a hypertrophy effect, you will be gaining strength through improving your muscles' efficiency rather than by increasing its size, the epitome of functional strength gains. It is important to follow this routine by lifting either 4 days straight or 6 days straight (if going 6 days straight, two exercises per day is enough.) It's like practicing a golf swing. You don't hit 500 balls once a week, you hit 100 balls 5 days a week.
You can also mix in some ballistic movements (either projecting a weight or medicine ball out of your hands or jumping or pushing yourself off the ground, i.e. jumping squats or ballistic pushups). This is best done with 10-30% of your 1rm. To make the proper adjustments for sports keep this in mind: ballistic movements increase your speed primarily and your explosive strength secondarily, whereas the oppposite holds for explosive movements. Maximal lifts are best for increasing overall strength, but not great for increasing speed very much. But since power is defined by how much weight you can move at a high speed, you need to build up your maximal strength in order to be able to move a significant weight quickly. This is especially relevant in sports that involve contact with other athletes such as football, rugby, or MMA.
Here's another analogy: a factory can get a lot done if it has a lot of workers, but a factory with less workers can get the same amount of stuff done if the workers are more efficient. Hypertrophy-targeted lifting will increase explosiveness and overall strength through an increase in size, whereas the above methods will increase explosiveness and strength by making you more efficient at recruiting motor units. It is also important to remember that when lifting explosively or ballistically, you should never be lifting to the point where the weight isn't actually moving quickly. If you lift explosively to fatigue, once the weight begins to move slowly, even if you have several more reps left in you, the fast-twitch fibers are done and the slower ones are taking over. It's okay to lift explosively IN a fatigued state, but not to lift explosively TO a fatigued state.
When doing maximal lifts, just make sure you can use the same weight for all sets with proper form. The speed the weight moves isn't important here as long as your form doesn't break down. For athletes, keep the rest short between sets (less than 2 minutes). If you aren't worried about maintaining a high heart rate and improving upon endurance, a rest of 3-4 minutes between sets (especially maximal sets) is fine.