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As far as modern lead guitar techniques go, sweep picking is the one that inspires both awe and fear. Listeners, viewers, and live audiences are spellbound by the sheer velocity at which masters of the technique are able to fire off arpeggios and scale fragments.
Now, while the sweep picking technique is undoubtedly impressive, it is also often the most difficult to master. However, once the technique is mastered, the possibilities become limitless.
The sweep picking concept is to play a rapid succession of notes, using one fluid up or down movement of the picking hand across the strings, without letting any notes ring into one another like a chord.
The Picking Hand
Often overlooked, the picking hand is, in my opinion, far more important and requires far more attention than the fretting hand, especially at the early stages of learning the technique. Most beginners will start trying to sweep by playing one string at a time, using one short upward or downward movement for each string. This common problem can be the reason why many guitarists never sweep quickly. Fortunately, this problem is easily remedied.
The easiest way to stop playing a succession of short up or down strokes, one string at a time, is to aim for the last string in the direction you are sweeping.
In the example below (a very simple A minor arpeggio) you would aim for the E string when sweeping downwards (ascending the arpeggio), and you would aim for the G string when sweeping upwards (descending the arpeggio). The idea is to sweep right through all 3 strings in one movement, without pausing.
This motion is made much more fluid by concentrating on another simple action. Make sure you are not sweeping with your wrist. Instead, keep your wrist stiff and sweep with your whole forearm, bending at the elbow. By doing this, you will only have to lean one position with your picking hand, then simply move it up or down by bending your elbow. Picking with a wrist action is great for fast and accurate alternate and directional picking, but getting comfortable with sweeping from the elbow early on will help greatly when learning sweep-tapping and 5, 6, and 7 string sweeps later on.
Using the elbow and keeping the wrist in one position also helps mute the adjacent strings that have just been played. The picking hand muting is done with either the outer edge of the palm or the thumb.
The Fretting Hand
The fretting hand positions are fairly basic when fretting one string with one finger: the fingers just follow each other up or down the strings. All you need to concentrate on is lifting your finger off the previous string just as you play the next string.
The tricky part comes when you need to fret 2 or more adjacent strings with one finger. This action is called "rolling". The aim here is to roll your finger from one string to the other, simultaneously fretting one string and muting the other.
In the example below, start by fretting the note C (5th fret) on the G string with the tip of your finger. Then roll your finger so that the tip lifts and mutes the G string, while the area halfway between the tip and the knuckle is fretting the B string. Now roll your finger a little more so that the tip and the area between the tip and the knuckle are muting the G and B strings respectively, and use the area closest to the knuckle to fret the E string. To sweep back up (descending the arpeggio), simply reverse the process.
Make sure that you mute the previous string just as you play the next one, ensuring that the notes do not ring into one another. I highly recommend you see the lesson on rolling by my friend and virtuoso guitarist, Zack Uidl here
For an interesting way to apply the sweep picking technique, please see my article, Introduction to Voice Leading, on combining major and minor arpeggios.