What is Tremolo Picking?
Tremolo means a modulation in volume; in the context of stringed instruments, usually refers to repeatedly striking or bowing a single string in a steady rhythm, especially the fastest rhythm the player can maintain. (This technique is particularly common on the acoustic mandolin.) In guitar literature, this is called tremolo picking, and one of the few places the term "tremolo" is consistently used "correctly" in guitar literature (whose convention usually reverses tremolo and vibrato). This technique has nothing to do with a "tremolo bar" (really a vibrato bar) or a "tremolo" effects box.
How to hold the Pick
Tremolo picking, though appearing hard at first, is actually quite easy. It is merely alternate picking at a faster speed. To start off, a pick makes tremolo picking much easier and is highly recommended when attempting it, but even though most people find tremolo picking much easier with a pick, it is possible without a pick. The best way to hold your pick is between your thumb and the side of the first knuckle of your pointing finger, but if you feel more comfortable holding it another way, such as with your thumb and middle finger then go ahead.
How to Pick
The movement should come mostly from the wrist. A little bit of arm movement is okay, but shouldn't be done intentionally. It is possible to tremolo with the elbow, but the wrist is actually easier and faster for most people with practice.
The motion done with the wrist should be like drawing quick zig zags, or Vs. Picking should feel just like writing. Imagine drawing as many connected V's as possible.
Do not play with your hand parallel to the strings. Pick like you write, with your wrist at an angle.
An important aspect of tremolo picking that many beginners fail to realise is that you must have a relaxed grip on the pick, as when you try to pick when holding the pick tensely, you will find that the pick hits the string harder therefore making it harder to pass through the string, causing it to sound sloppy. Maintaining a relaxed grip becomes harder when playing faster, but you will get used to it.
Things to Remember
When tremolo picking make sure you use just your wrist, as this will make it much easier to pass through the string. Also, when you pick the string, make sure your hand doesn't go to far away from it, as this will slow you down. The impact from hitting the string usually forces your hand to leave the string, but after practice, avoiding this will become easier.
It's also important to remember that many beginners start to use the thin side of the pick to tremolo, since the thin side has a smaller surface area and passes through the strings easily. This is incorrect, as the pick start to not only damage the strings, but also causes damage to the wrists, and may further start to ring other strings. Use the flat side of the pick to tremolo, not the thin border.