Check out youtube for lessons my Micahel Angelo Battio, possibly the best advice I have ever seen/heard re picking speed.
Basically, you pick any string as fast as you can up and down (alternate picking), don't bother with the left hand, just the right. You want to go as fast as you can keeping a straight rhythm. You can make it easier when you start out by adding an accent to which ever note you are most comfortable with (I recommend playing groups of 4 with the accent on the first: DOWN up down up DOWN up down up etc.)
What this exercise does is establish your maximum picking speed, at any given time that is the fastest you can possibly pick. Try it to a metronome and you can work out exactly how many notes you can play per bpm.
I used to do that exercise for about a minute before playing anything and I found that I was able to significantly increase the speed of my right hand by taking the left hand out of the equation.
The most difficult part of playing fast comes next and that is synchronising the left and right hand. If you can't play it accurately slowly then don't try to do it any faster. When you get it down at say 150 bpm you can then work on increasing the speed gradually to meet your maximum picking speed eg. 200bpm.
Hope that helps.