Let not overcomplicate this. You coach speed into the athlete by training speed at the appropriate time in the workout, using an appropriate method and dosage for the time of the training year. You train speed out by doing all sorts of general nonspecific work and slow “base building” type of work, in short emphasizing volume.
Remember you are what you train to be! To be fast you must train fast. When I hear a coach say I have not started speed work yet, I just smile, and I hope we can compete against those teams or individuals often. You train speed from the first day of training until the last. Remember the stimulus for speed is high quality intense work. It does not take much to dull speed.