A fretboard diagram is a grid pattern of strings (vertical lines) and frets (horizontal lines) which is used to indicate the position of notes.
The dots show you where to place your left hand fingers, and also which string to play with your right hand.
The white letter inside the dot tells you the name of the note you are playing. The dot is placed in the same position that you should place your finger. If the dot is above the nut, play it as an open (non fretted) string without placing your finger on the fretboard.
A diagram with colored dots indicates the notes are from one of the three basic types of tonality used for chords and scales: major (shown as red dots), minor (purple dots) and dominant (green dots). For more on scales see The C Major Scale, and for more on chords see Arpeggio Playing. Gray dots are used when the notes are not part of a chord or scale.