Originally Posted by ShredOrDead
Learn the major scale all over the fretboard, in every mode, in every key. Learn 3 and 4 note coils (ascending and descending). Play them using alternate picking and sweep picking, and pick every note. That's what I did (also with harmonic minor and pentatonic), and it makes playing other people's shred stuff much easier. Just my $0.02.
The only thing I would add is play with a metronome. I know it is boring but I when I went to Musicians Institute I seemed to hear the same story from guys like Paul Gilbert to Al Di Meola to Frank Gambale say the same thing. To get fast and clean there is only one route to go.
Take the 7 modes. Play them all in A, 2 octaves each mode, starting at the 5th fret, going up the fretboard with the root note on the 6th string. Now with the metronome at a low rate, like 60, play each note on the fretboard with the click. Everyday put the metronome up 2 more clicks and keep playing it until you are perfectly accurate. Don't increase the motronome until you are playing perfect. Within a few months you will be shredding like crazy.
If this is too hard, first try the 4 notes per string, one note per finger exercise that you start on the low E string, 1st fret and go all the way up and down the fretboard with the metronome.
Also, if you can find it, check out that old Paul Gilbert video lesson tape thing. He figured out some really cool shredding licks and patterns that are easy to pick up and when they are played fast...WOW!!
Hope this helps