there are two things affecting how quikly you can fret or pick; how far u have to move the pick and how quikly your hand moves.
i shall talk abou the picking (right) hand. you want to move your hand as little as possible to make the note. this can first be helped by getting a thick pick as it bends less and is therefore able to make smaller motions to pluck the string. also only letting a small part of the pick show will also speed you up as it will flex less. futher more try to make your picking motions as small as possible. this can be done by picking by moving your wrist instead of picking by moving your elbow. as your wrist movements can be far more acurate.
next is how fast you move your hand.the first thing to say about this is relax. if you are tense the contractor and extensor muscles act against each other, slowing each other down. its like trying to accelerate with your foot on the brake. this is a hard thing to do as you will probably find as you speed up u tense up. what i advize is play as fast as you can relaxed. just pick the same note over and over. a good idea is watch tv whilst doin this. it makes it less boarin and as you are watching tv u should be relaxed. again picking from the wrist is advized as moving your hand up and down takes less force than moving your hand and your forearm.
note when picking from the wrist use the elbow joint to move the pick to watever string you are picking and use the wrist tio actually pick.
this should help you pick faster. but again all you can do is practice pratice practice. use a metronome and practice just below the speed you tense up, then slowly push the speed trying to stay relaxed.
if the problem is with the fretting left hand, or coordinating the two hands, just ask.