Learn the names of the six strings and their corresponding octaves. An octave is the same tone as the original, just eight notes higher. From lowest pitch to highest, the string notes are E A D G B E. For the two lowest strings, the octave is played two strings up, two frets down. For example, the open E on the sixth string has an octave at the second fret on the fourth string. There are also octaves at the 12th fret on every string, usually the double dotted fret on most guitars.
Practice finding one note at a time all over the fretboard. For example, devote a practice session to finding E on all strings. The better you get at not having to think about where any given note is, the faster you will be able to memorize all eight tones on the music scale.
Use flash cards. Try writing down the notes for each fret of the guitar. For example, the third fret would be: G C F Bb D G. Work your way up the entire fretboard, playing the notes as you go to enhance your memorization.
Play some basic chords, pausing to name each note in the chord. At this point, you've practiced naming them in a straight vertical line, but can you rattle off everything you're playing in a G major chord? Practice all of the major chords, and try to get to the point where naming all of the notes you are playing is second nature.