What factors play a role?
There are two primary muscle fiber types: slow-twitch and fast-twitch fibers. Fast-twitch muscle fibers contract to maximum force more quickly than slow-twitch fibers. In general, world class sprinters would be expected to have a predominance of the fast-twitch muscle fibers(eg. 60-90%) while a long distance runner would have a majority of fibers in the slow-twitch category. Genetics is the primary determinant for an individual's percent of fast vs. slow-twitch muscle fibers. Proper training can affect fiber size as well as the number of sarcomeres in muscle fibers. The majority of research indicates that while speed has a direct correlation to genetics--it is possible to improve on what nature has already given you. 

What can you do to improve your speed? 
 Speed drills, interval training, resistance training and plyometrics  are techniques used for cross training for specific sports. 

Speed Drills - Drills should focus on the types of movements associated with soccer. Some of the following are commonly used: 
  Sprinting up hill - this sprinting exaggerates the runners stride and particularly targets the forward run. 
  Running backwards - short races while backpedaling help in scenarios where it is needed to face the ball. 
  Lateral motion - (at least 2 people needed) one person with a whistle, should blow the whistle and point in a direction, while  the runner moves laterally. (This also works well for forward and backward motion). 
  Exaggerated skipping - this skipping is more like a single leg bound with the knee in the air. 
  Sprint with back kicks - exaggerating the back kick motion when running. 

Interval Training - Manipulation of rest intervals between repeated sprints is a common training technique. 
  -complete a group of short sprints (distance could be 20-200 yards) in sets. A sample structure would be to run 3 sets of 3 with a rest of 40 seconds in between runs and 3 minutes between sets. 
  -use pick-up sprints for a one-to-one distance between sprinting and recovery time (e.g.. run 30 yards, walk 30 yards) 

Resistance Training - In general, it is recommended to weight train at a moderate-to-high intensity at least two days per week for a minimum of one set of 8-12 repetitions. Resistance training should include the lower body muscles and be well-balanced--many injuries occur because of an imbalance between opposing muscle groups. 

Plyometrics - Plyometrics was a popular training technique with the Russians. It was commonly known as "jump training" or "shock training". This training focus is based on very fast, explosive exercises that utilize the Stretch-Shorten Cycle where the muscle is rapidly stretched and contracted, thereby causing an increase in applied force.(please note: plyometric exercises are very intense and should not be done by those who have had little weight training or cardio fitness work). 
  Hopping - hop on one leg for a distance of 10-15 hops. 
  Serial Bench Jumps- with both legs jump over a series of benches (eg.3 or 4). 
  Side Jumps - using a bench (step), jump laterally from one side to the other (best performed on a soft surface such as grass to minimize the pressure when landing). 
  Split jumps - in lunge position, switch leg positioning while in air. 
 
 

"Plyometrics", John Imison www.vision.net.au/~jimison/plyometrics/plyo.html
The Plyometrics page at: www.spinalhealth.net
Carr, Gerry,"The Fundamentals of Track and Field" available at: www.amazon.com
Chu, Donald, "Jumping into Plyometrics" available at: www.amazon.com
"The Personal Trainer Manual" from the American Council on Exercise-available at: www.acefitness.org