Form: Watch olympic sprinters... study everything. Perfect your form. That's the most important thing.
So true I can't say much more about it.
Quickness: This is more important in soccer IMO. Do you have an agility ladder? I suggest getting one of those and working on that everyday to increase your foot quickness.
I call it "speed workout." Yeah, doing sprints helps whether you play soccer or run distance or whatever (XC runners unite!)
Strength: Strengthening your core, shoulders, and legs will ultimately make you more explosive and a powerful runner.
Indeed.
Flexibility: Flexibility is overlooked. The best sprinters are all flexible as shit. Stretch several times a day like a madman and this will increase your speed and quickness. Flexibility gives you better turnover (in addition to making you less likely to pull something!) and stride length since your muscles can contort more.
Yep.
Running is 50% mental, 40% cardio, and 10% abs, or so we say. If you got the mental half down, you're pretty much set for life.
EDIT: Luphrous, advice for you.
For speed, I do speed workouts every Monday. However, I'm a distance runner, so you may need more, or more reps of a shorter distance. A speed workout is typically composed of 800's, 600's, and 400's (in meters- about a half-mile, 3/8s of a mile, a quarter mile if you're unmetric like me) run in groups, with a brief recovery in between. Start with some 800's- at the beginning you'll probably just do two. The recovery between each should be walking about 100m, then coming back. Do not sit down, ever, as this locks up your muscles. Then you can do a couple 600's and 400's. Same recovery, etc. If you need less speed for longer sprints and you're going for more of a "hundred-meter dash" (I'm not sure which one you would need in soccer) you can tone it down to 400's, 200's, and 100's. You don't need to buy stuff off the internet, you just need good running shoes which you can find from a local store.
As for how often, do some kind of workout every day. One rest day a week is plenty, you don't need more than that.
And as for the "best way to work out" that everyone is asking, it depends what you're trying to do. Running and some weight lifting works fine- but if you're a runner, you don't want to get too buff.