Notes on the guitar fretboard are preset. The guitar is a tempered instrument, meaning that the notes we have as choices to play are set beforehand. The violin, the trombone, and the human voice are all examples of non-tempered instruments. On these, the player (or singer) has an infinite choice of possible tones and notes to play (or sing).
The piano and the guitar, however, follow the standard 12 tone equal-tempered system. This means that we have 12 tones to choose from. Those tones may repeat an octave higher, or lower, giving us a different note, but those 12 tones are all we have.
The only way to play a tone outside of this 12 tone system is by bending a string, using a trem bar, or detuning your guitar.
On a guitar, each fret is one step in that 12 step system. If you play two contiguous frets on the same string, one after the other, you'll hear the interval of a semitone (or minor second).
If you skip one fret, the interval is one whole tone (major second).
Guitar Notes Image 1: a Semitone and a Whole Tone
If you play any 12 tones next to one another —12 consecutive frets— what you get is a chromatic scale.
We will call the nut "fret 0", as it also counts. This means that if you start on any open string, and go up fret by fret, you'll get all the tones of the chromatic scale by fret 11 . Remember, the open string also counts, so 1 + 11 = 12.
The cycle starts again beginning at the 12th fret, an octave higher.
Guitar Notes Image 2: the full Chromatic Scale
What about the guitar's "height", relative to other instruments?
This is key, whether we play alone or with others. It is especially important whenever we play with other musicians, whether singers or instrumentalists.
Most guitar sheet music shows a treble clef. For this reason, guitarists in general think that they have a very high pitched instrument. But a violin is higher pitched than a guitar! And violin music is also written in the treble clef!?!? 
What most editions of guitar sheet music don't say, is that guitar music is not written in treble clef, but in tenor clef. It looks exactly the same as the treble clef, except that it has a little "8" underneath, meaning that all notes on the guitar fretboard are an octave lower:
Guitar Notes Image 3: Piano Notes and Guitar Notes compared
This means that middle C on the guitar is located on the first fret of the second string, NOT the third fret of the 5th string! This simple fact shocks even professional guitarists who have been playing for years. I've met some stubborn enough to deny it altogether (virtuosos, too!). If in doubt, simply go to a piano and see for yourself!
Still unclear? The following diagram shows the open strings of the guitar as written in guitar notation, and standard, non-transposing notation:
Guitar Notes Image 4: The open strings of a guitar, as written in
guitar sheet music and piano sheet music
If, say, you're playing with a keyboard player and you want to communicate with him, you'll want to be able to tell him what your open strings are on his instrument. Or if you want to write an arrangement, you'll need to get all your instruments' parts properly distributed by note range.
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