Google says the flight time achieved while running is the largest difference between athletes and us commoners, so I'd like to focus on these muscles alittle. What muscles do we use to launch off the ground?
tl;dr- Core, everything below the waist, and throw in your arms.
A coordinated running stride uses the arms for counterbalance, and the shorter or more intense the speed, you will use them for drive as well. The core keeps your balance, and obviously the legs are used.
The primary drivers in the legs will be the quadriceps, hamstrings, glutes and calves. Hamstrings work with the hip flexors to bring the lower leg up and swing it forward at the beginning of the leg cycle, quadriceps extend the leg, glutes help bring the leg backwards/the body forward during the plant, and the calves push off the ground at the end of the drive phase, which gives you the "flight" phase.
So. Now, the flight time and leg stiffness (Helps get more energy from the ground/rebound) are what you need to train. Air time can be gained simply by adding high speed running such as hill sprints, intervals and fartlek type running. Leg stiffness can be increased by plyometrics and lifting. Just be sure that you don't overlift, large heavy leg muscles are a detriment when doing longer (2 mile and up) racing.
The biggest thing is if you are a heelstriker, switch to a mid foot strike. By that, I don't mean what part of your foot touches first, but what part of your foot is bearing the most weight when your center of gravity passes over it. A heel touching first (Especially with more padded shoes) may or may not indicate a heel strike stride. That's best determined by a video, which any decent larger running store will have.
Speed drills, plyometrics, and heavy lower body lifting (to a point) will all be what you want to work on.