Notes on the Guitar:

All of the notes on the guitar are labeled by letters of the alphabet, from A to G.  The notes on the open strings are:

6 = E  (The thickest, lowest sounding string)
5 = A
4 = D
3 = G
2 = B
1 = E  (The closest string to the ground)

The string names can be remembered with the phrase "Eat A Darn Good Breakfast Every day" (from 6 to 1). 

All of the letter names on each string are seperated by either 1 or 2 frets:

A  B  C  D  E  F  G  A  ...
  2  1  2  2  1  2  2

Notice that B-C and E-F are seperated by 1 fret.  All of the other notes are seperated by 2 frets.  Knowing this enables you to label every note on the guitar!  Try it:

The open 6th string (0 fret) is E.  One fret up from an E is F (1st fret).  2 frets up from F is G (3rd fret).  Two frets up from G is A (5th fret), and so on ...

The letters seperated by 2 frets all have an "in between" note labeled by either a "sharp" or "flat":

Sharp:  #  -  moves a note up 1 fret

Flat:    b  -  moves a note down 1 fret

So, the note in between F and G can be called either F# or Gb.  Between A and B, the note is called either A# or Bb.  The set pattern of letter names creates a complete musical system of only 12 note names:

A
A#/Bb
B 
C
C#/Db
D
D#/Eb
E 
F
F#/Gb
G
G#/Ab

The notes repeat every twelve frets on each string - at G#/Ab, they start over again with A.  Notes that are twelve frets apart are called octaves.  They have the same note name and sound, just in higher and lower pitch registers (imagine a man a woman singing - they can both sing the same melody in octaves - the man sings in a low octave, the woman sings in a high octave).

Study the diagram below until it is clear how the notes on the fretboard are labeled, and how octaves work: 

(fretboard note diagram)