Tom Kurz' book Science of Sports Training has a good chapter on speed training, with oodles of studies backing it up. One relevant section is on page 191-192:
A well-trained athlete must rest 5-8 minutes between sprints of up to 100 meters if the number of repetitions is not excessive. Because these rest intervals are so long, besides passive rest light exercises similar to or imitating the main exercise are done while the athlete is recovering to maintain the specific neuromuscular coordination for the main exercise.
According to Naglak (1979) speed exercises should be done in small doses but frequently, even several times during the day, but in varying form and in different conditions and not too often at the maximal speed.
That last part about avoiding full-time work at maximal speed is in order to prevent a "speed barrier" from forming, which is discussed in more detail in the book. There is literally an entire chapter on this specific topic, so I recommend reading the book or narrowing down the question. Personally, as someone using sprints for other sports and fitness purposes, I do three to six sprints with anywhere from thirty seconds to a few minutes between them.
Keep in mind that speed training is distinct from power training, and the set/rep/rest schemes that work for barbells are not the same as those that work for interval sprints, kettlebells, and so on.
The element of weight training that you want for speed is power. Power is optimally developed with a moderate number of reps (e.g. 3-6) done with near-maximal bar speed (though pauses between reps are fine) and submaximal loads. For the goal of optimal sprint times, that might mean five sets of three power cleans or snatches done at 60% of your 1RM, or four sets of four at 70%, or similar. I'd also make sure to work on maximal strength, which in the context of running would mean a handful of near-maximal deadlifts. For instance, one heavy set of 3, five singles, a maximal set of 2, or similar.
For sprints, the takeaway I got from Kurz' book was that the best way to train speed was to take complete rests between sprints. One would still do longer runs and sprints where one was not fully rested, but maximal sprints seem to develop best when fully rested but not cold.