To play fast with a pick I assume that you are talking about trem-picking (if that isn't the proper term then forgive me. Everyone here uses that term). That's basically picking up and down strokes very quickly i.e. John Petrucci. To do this effectively, here are some tips:
-Rest the bottom of your hand on the bridge or someplace else convenient. Don't mute the strings.
-Only hold the pick with your thumb and index finger. The reason for this is efficiency. If you use any other finger combinations than that then you'll have to use your entire fore-arm for the picking motion whereas you'll mostly use your wrist if you hold the pick with only your thumb and index finger.
-Pick at a distance from the bridge so you can keep the bottom of your picking hand rested on the bridge while not picking too close to it.
With all of this in mind, just play alternating up- and down-strokes until you can do it steadily. Once you're steady then you can start developing your speed. Go for steadiness first, not speed. Only speed up once you can pick steadily at low speeds. I hope this all helps.
