Many believe the truest type of speed training is that which improves your VO2 max. VO2 max is the amount of oxygen your heart can deliver, via the blood, to the working muscles when at maximum capacity. VO2 is usually tied to a relative value such as body weight for easy comparison.
VO2 max is still generally accepted as the best indication of overall cardiovascular fitness, with higher values indicating greater capacity for endurance and performance. University and specialty sports labs will often perform (for a fee) VO2 max tests on a treadmill using an incremental exercise test.
All running, easy or otherwise, will ultimately act to improve and maintain your VO2, but specific workouts and types of training can be used to really push it.
One way to do this is short and fast intervals with very little rest, done on a flat stretch of road or a track.
30/30s and 60/60s are examples of this. To do them, run for 30 seconds building to a very quick pace, then take 30 seconds to recover by running or walking very easy. Start with 10 repeats back-to-back and gradually aim to build up to 20. Be sure to warm up and cool down before and after the intervals. You can also run 60-second repeats and take 60 seconds of rest. In this case, start with five repeats and build up to 10.
Hills are a great substitute for flat intervals. Find a hill of medium grade and run repeats of 60-90 seconds with an easy jog back to the bottom. Start with five repeats and eventually built up to 10.
VO2 max workouts, when done right, are extremely tiring and should leave you feeling exhausted. Give yourself a day or two to recover and reap the much-deserved adaptations. One VO2 workout a week should be enough but those wanting quick improvements (and who are not prone to burnout or injury), could attempt two workouts a week.