Race / Hard Effort Warm-Up
Some of this is going to be elementary, but it's best to document it. Many runners will do a mile of easy running and then attempt to do their workout / race - rumours have it that some people even race without warming up at all.
A mile of easy running is not even sufficient to raise core temperature during winter let alone prepare your body for hard running. A race requires a an easy warm-up of at least 2 miles, followed by strides. Strides are necessary to prepare your body for the harder running without incurring undue fatigue, they also put your body through the full range of running movement reducing the likelihood of ROM related strains. You will find your performance improves just doing those two things.
However, to do this in races means you must also prepare by doing them in training. The goal is to be ready to go with your hard workout / race and to be fit enough that achieving this state doesn't fatigue you.
The bare minimum that I will insist on before hard workouts / races is 2 miles of easy running plus 3 * 20 second strides with 40 second jog recovery. For higher mileage and faster athletes (I only bring speed into it because 2 miles for one athlete may take as long as 3 for another) 3 miles is a minimum.
Exceptions
Race exceptions: Marathon where you will do the bare minimum.
Training exceptions: MP / progressive runs where, because of the gradual developing pace of the workout, strides can be foregone if absolutely necessary.
Additions
Many warm-ups should include the use of drills and dynamic mobility exercises. These are particularly useful for workouts at 3k pace or faster. More on these later and they have to be integrated judiciously.
An Example
I will use myself as an example for a track workout, not because it's ideal, but because it's tried and tested and gives you an idea.
3m easy warm-up, progressive
5 * (50m drills, 50m jog back, 50m strides emphasising the drill technique, 50m walk). Each set is a different drill. (I should be adding some dynamic mobility into this also).
0.5m of jog the turns of the track and striding the straight.
Start workout......