When you increase the strength in your legs and hips, you will automatically improve your ability to produce force, which results in increased explosiveness. The more force you can exert against the ground---the higher your ability to jump.
It is extremely important for a strength training program to be safe; nobody can jump higher when they are injured. To reduce orthopedic stress while strength training, you should work within an appropriate repetition range. For most football players, sets with 6-15 reps are usually appropriate. You should avoid maxing out (seeing how much you can lift for one repetition) as that can be extremely dangerous.
You should aim to make every strength training workout brief, yet very intense, just like each play in a football game. A strength program should focus on training the entire body equally to ensure muscle balance, as well as having each exercise taken to the point of momentary muscular fatigue (the point at which no further reps can be achieved). Training at a high level of intensity will produce maximum results in the shortest time possible. All of this can be accomplished in two or three well-planned full body workouts per week, each lasting about an hour.
As obvious as it sounds, if you want to be able to jump higher, you need to practice jumping as high you can.
Plyometrics are exercises that usually involve some form of explosive movement such as a jumping, hopping, or bounding and are designed to increase power and explosiveness. If used appropriately, plyometrics can be a great tool for increasing your vertical jump. These exercises usually use the force of gravity to store potential energy in the muscles, and then immediately release this energy in the opposite direction--similar to pulling a rubber band back before you fling it. The energy stored is used to produce a more powerful muscle contraction--in other words, a more "explosive" movement.
Plyometric exercises such as jumping, skipping, and bounding--if incorporated appropriately--provide a means for you to practice jumping with maximum effort in a controlled and safe environment. Additionally, a proper plyometric program can help train your nervous system to perform athletic movements more efficiently. These exercises and drills should be chosen carefully and be done in limited volume. Attempts should be made to reduce as much impact and orthopedic stress as possible, so try to use soft training surfaces, make sure you are wearing proper footwear, and know that when it comes to plyometric training, more is not necessarily better.
Squat jumps, broad jumps, and box jumps are some common plyometric exercises used to increase your explosiveness and improve your vertical jump. When performing box jumps, it is highly recommended you jump on to the boxes only; not off of them. You should step down off of the boxes to eliminate as much impact as possible. It is important to note that these exercises should be performed when your legs are fresh; so do them before a strength training workout if both workouts are being performed one after the other.
When most athletes think of their "jumping muscles" they think of their legs and hips. However, your core (abs, low back, hip flexors) play a huge role in jumping. Your core is the center of every athletic movement, including jumping. To truly maximize your vertical jump, you need to have a strong core. The days of lying on your back and just doing regular crunches are long gone; you need to stimulate yourself with new and innovative exercises to work your core from a variety of angles and motions.