I still don't understand why more athletes and coaches won't invest in the general physical preparedness of their athletes, but would rather shell out their hard-earned cash on "sport-specific" gadgets and gizmos that won't do anything to get them stronger and moving better. I'll take it a step further and say that the younger the athlete, the further away they should stay away from specialized "sport-specific" training centers and spend more of their time training with a competent strength coach or trainer to help get them stronger, resistant to injury, increase body awareness, etc.
Instead of focusing solely on 1 sport, year-round, I would like to see more young athletes participating in 2-3 sports while being involved in a properly designed strength and conditioning program. It used to be normal and encouraged that athletes participate in different sports each season, especially at a younger age. Nowadays, it's not uncommon to see athletes specializing in 1 sport in high school, or even worse, in middle school. Playing multiple sports is a form of "cross-training" and helps to create athleticism, spatial/body awareness, and more importantly, prevent boredom and burnout.
OK, back to the topic at hand. Weight training for speed and power is pretty simple and needs to be focused on large, multi-joint movements first. Think about training movements and movements in multiple angles and planes, not just training muscles. To keep things very simple, you should devote each weight training session to training the entire body. Once you get stronger and more mature, you can start to break up the training into upper and lower body workouts, but for now, most athletes would do just fine performing full-body sessions. You'll break the sessions down by movements (I got some of these basic principles and guidelines from Jason Ferruggia, owner of Renegade Strength and Conditioning in NJ):