Guitar/Muting and Raking
Muting a string is simple: with the fretting hand, touch the string with a finger, but do not press it down, and strike the string. It is usually best to do this where a harmonic will not result, but strings can be muted at harmonics for special effect. In tablature, muted notes are often marked with an "x" instead of a fret number. It is also common practice to mute a string with the picking hand after striking a note to create a shortened "staccato" effect. Again touching a string to mute away from harmonic nodes is advised, but sometimes pulling off into harmonics creates interesting effects.
Palm muting 
Palm muting may or may not make the pitch of the string discernable. Very lightly rest the palm of the hand on or near the bridge, then fret and strike strings normally. Palm-muted notes are sometimes notated the same way as muted notes when the pitch is not discernable; otherwise fret numbers are given normally and the muted notes are marked "P.M." in tablature.
The Palm Muting Technique 
The idea is not to mute the strings, but to dampen them, so that the notes are still clear, but with less sustain. To start, hold your guitar like you normally would, but let your palm brush against the strings, near the bridge. Remember to "let" the strings brush against your palm, not putting any force on the strings. The closer to the bridge, the more forgiving it is. As you get better, try adjusting the amount of muting by keeping your palm at different distances from the bridge. Very heavy palm muting can raise the pitch of the note(s), especially on guitars with a floating tremolo bar system equipped. Using or not using this effect is at the reader's discretion.
Finger Muting 
You can also mute strings just by pressing your fingers against the strings, but not so hard that they are fretted and play notes.
Raking is not a kind of muting, but a technique for applying it. It is vaguely related to sweep picking, but instead of an arpeggio, the result is usually a single percussive-sounding note. (However, sweep picking is sometimes incorrectly notated as a rake in tablature, and sloppy sweep picking may accidentally become a rake.) Between two and four strings are struck, only one containing the desired note and the rest muted. Rakes may be notated in various ways; the most common way is to add muted grace notes, possibly adding the word "rake" to the tablature for clarification.