Learning to speed pick can be quite difficult. Many guitarists do it different ways from circular picking to stiffening their arm and wrist. I recommend trying to keep your arm and wrist as loose as possible and let the movement come from the wrist. Try to minimize the range of motion.

The following exercise is done in 3 parts. Each one should be repeated starting on the 12th fret and working down the neck until you hit the first fret. Then you should move to the next string and repeat until you have played the exercise on each string. I also highly recommend using a metronome to stay in time and focus on keeping the notes even. Find the starting metronome tempo by seeing at what speed you can comfortably play 16th notes, then go back and start with the 8th notes.

8th Note Speed Picking

First, start with 8th notes, just two picks per note.

   1  +  2  +  3  +  4  +    1  +  2  +  3  +  4  + 
e|-15-15-12-12-13-13-12-12-|-14-14-12-12-15-15-12-12--|
B|-------------------------|--------------------------|
G|-------------------------|--------------------------|
D|-------------------------|--------------------------|
A|-------------------------|--------------------------|
E|-------------------------|--------------------------|


   1  +  2  +  3  +  4  +
|-14-14-11-11-12-12-11-11-|-(etc.)-|
|-------------------------|--------|
|-------------------------|--------|
|-------------------------|--------|
|-------------------------|--------|
|-------------------------|--------|

8th Note Triplet Speed Picking

Now increase the complexity a bit by adding a third note to each beat and play 8th note triplets.

   1  +  a  2  +  a  3  +  a  4  +  a
e|-15-15-15-12-12-12-13-13-13-12-12-12-|
B|-------------------------------------|
G|-------------------------------------|
D|-------------------------------------|
A|-------------------------------------|
E|-------------------------------------|


   1  +  a  2  +  a  3  +  a  4  +  a
|-14-14-14-12-12-12-15-15-15-12-12-12-|
|-------------------------------------|
|-------------------------------------|
|-------------------------------------|
|-------------------------------------|
|-------------------------------------|


   1  +  a  2  +  a  3  +  a  4  +  a
e|-14-14-14-11-11-11-12-12-12-11-11-11-|-(etc.)-|
B|-------------------------------------|--------|
G|-------------------------------------|--------|
D|-------------------------------------|--------|
A|-------------------------------------|--------|
E|-------------------------------------|--------|

16th Note Speed Picking

Now add a fourth note, essentially doubling the first version of this exercise. At this stage, it really helps to think of the notes as not faster, but rather shorter.

   1  e  +  a  2  e  +  a  3  e  +  a  4  e  +  a
e|-15-15-15-15-12-12-12-12-13-13-13-13-12-12-12-12-|
B|-------------------------------------------------|
G|-------------------------------------------------|
D|-------------------------------------------------|
A|-------------------------------------------------|
E|-------------------------------------------------|


   1  e  +  a  2  e  +  a  3  e  +  a  4  e  +  a
|-14-14-14-14-12-12-12-12-15-15-15-15-12-12-12-12-|
|-------------------------------------------------|
|-------------------------------------------------|
|-------------------------------------------------|
|-------------------------------------------------|
|-------------------------------------------------|


   1  e  +  a  2  e  +  a  3  e  +  a  4  e  +  a
e|-14-14-14-14-11-11-11-11-12-12-12-12-11-11-11-11-|-(etc.)-|
B|-------------------------------------------------|--------|
G|-------------------------------------------------|--------|
D|-------------------------------------------------|--------|
A|-------------------------------------------------|--------|
E|-------------------------------------------------|--------|

16th Note Triplet Speed Picking

For the trickiest challenge of all, add two more notes to make 16th note triplet groupings of 6.

   1  e  a  +  e  a  2  e  a  +  e  a  3  e  a  +  e  a  4  e  a  +  e  a
e|-15-15-15-15-15-15-12-12-12-12-12-12-13-13-13-13-13-13-12-12-12-12-12-12-|
B|-------------------------------------------------------------------------|
G|-------------------------------------------------------------------------|
D|-------------------------------------------------------------------------|
A|-------------------------------------------------------------------------|
E|-------------------------------------------------------------------------|


   1  e  a  +  e  a  2  e  a  +  e  a  3  e  a  +  e  a  4  e  a  +  e  a
e|-14-14-14-14-14-14-12-12-12-12-12-12-14-14-14-14-14-14-12-12-12-12-12-12-|
B|-------------------------------------------------------------------------|
G|-------------------------------------------------------------------------|
D|-------------------------------------------------------------------------|
A|-------------------------------------------------------------------------|
E|-------------------------------------------------------------------------|


   1  e  a  +  e  a  2  e  a  +  e  a  3  e  a  +  e  a  4  e  a  +  e  a
e|-14-14-14-14-14-14-11-11-11-11-11-11-12-12-12-12-12-12-11-11-11-11-11-11-|
B|-------------------------------------------------------------------------|
G|-------------------------------------------------------------------------|
D|-------------------------------------------------------------------------|
A|-------------------------------------------------------------------------|
E|-------------------------------------------------------------------------|


|-(etc.)-|
|--------|
|--------|
|--------|
|--------|
|--------|

If you can’t play all of these up to speed, then slow it down and work your way up. This will take quite some time, so don’t expect to shred the first day. Over a few months, you should be able to work up your speed slowly. Don’t try to take big jumps or you will suffer in accuracy and technique.