Chords in standard notation
Especially in classical music, standard notation is used for guitar (although tablature can be used as well).
With and without doublings
Triads (the most common forms of chords) include three notes. But in practical use in context of many instruments including the guitar, more than three notes are involved when playing these chords. Only playing three happens, but it’s more common that one or two notes of the chord is doubled. The two diagrams (fig. 1) illustrate a C major triad without and with doublings:
fig. 1 C triad in standard notation with diagrams.
In the second diagram, the C and E notes are doubled (which would involve the 1st and 2nd strings played in open position). The second way is a more natural way to play the chord on the guitar and it gives a richer sound.
The next two diagrams (fig. 2) illustrate a G major triad without and with doublings:
fig. 2 G triad in standard notation with diagrams.
Compilation of triads in standard notation (pdf)
Arpeggio is common in classical music. See this illustraded in figure 3 as an example in G major:
fig. 3 A short arpeggio.
An arpeggio is sometimes notatied with a vertical wavy line, with an arrow pointing down or up depending on the direction. This indicate that the notes should be played in a rapid sequence. The figure 4 with sound example illustrate this:
fig. 4 A rapid arpeggio.
In classical music, the letter "C" indicates a barre chord or at least that the string should be barred. Often is the C followed by Roman numerals, which tells the position of the barre. In addition, numners are given of how many strings that should be barred. Whereas only a C may indicate a full barre, "1/2 C" will indicate a half barre.