One of the first things to consider when approaching the alternate picking technique is the choice of plectrum. Naturally, variations in thickness, materials, and sizes in different picks yield different results different results. Some may work better for certain techniques or styles than others.
When it comes to melody playing, including the alternate picking technique, it is advisable to avoid extra thin picks -probably a .60mm gauge would be a good start. Regular sized picks are also a good choice for beginners, as small picks tend be easier to drop. As picks become thicker and thicker, they loose their flexibility, and for some guitarists this translates to a lesser capacity to strum in a natural, flowing way (or at least it demands that the player puts more attention to it). The loss of flexibility also implies the loss of the subtle sound the pick makes when it bends, which is an added value when recording strummed guitars. On the other hand, thicker picks respond better to subtle movements, permitting the small and fast movements required for speed playing. Even if the goal isn't speed, they offer more control over the tone and articulation.
One of the most commons way to hold the pick is letting it rest on the side of the tip of the index finger, and securing it there with the thumb, which should be in an almost 90 degree angle in relation to direction of the pick tip. This is one of the traditional grips, though they vary slightly from player to player. That being said, some famous guitarists hold their picks in surprising ways (Eddie Van Halen holds it between his thumb and middle finger, Pat Metheny uses it backwards, James Hethfield uses three fingers, Brian May uses a coin, and Jeff Beck doesn't use one at all).
When sitting, the top of the right forearm will help hold the body of the guitar, as in the classical position. This leaves most of the forearm, as well as the wrist and hand, free to move. Guitarists differ on how to approach the actual alternate picking motion: some recommend initiating the movement at the elbow, and some at the wrist, with the latter being the most common choice. It seems only natural that the farther from the pick the movement initiates, the harder it becomes to make subtle movements. Following that line, some guitarists opt for the circular motion technique, with the bulk of the movement concentrated in the thumb and index that hold the pick. Guitarist also differ on the position that the rest of the right hand should take, with some recommending resting the little finger on the body of the guitar.
The pick should not attack the strings in a perfect 90 degrees angle, as this usually results in a stiff and awkward motion. It is preferable to employ a slight declination on the wider side of the pick instead, always considering that the more 'slicing' the movement, the less clear the attack. The point where the pick makes contact with the string is also something to take into account: as when playing fingerstyle, attacking near the neck will produce an opaque, mellow sound. As the pick approaches the neck the sound will become increasingly brighter, with more harmonics standing out. This becomes a very important issue when dealing with pick-produced pinch harmonics.
It is advisable to practice every alternate picking exercise with different levels of palm muting. Even muting the strings is not always a need, it can come in handy when playing at great speeds or with intensive distortions, as it helps remove unwanted noise. Resting the heel of the palm of thee bridge of the guitar will do the trick, and varying the pressure will, in turn, act as a turning a knob on the palm muting.