I know there are many other lessons and methods of learning the notes of the fretboard. I have seen a couple of these (but not all of them) but they seem harder than it all needs to be. As long as you know your alphabet up to G you can learn all the notes on the fretboard in a few minutes.
So lets look at the A-string (just for sake of staying in alphabetical order and therefore being more memorable) the notes on this string are as follows:
0 1 2 3 4 5 6 7 8 9 10 11 12
A, A#/Bb , B , C , C#/Db , D , D#/Eb , E , F , F#/Gb , G , G#/Ab , A
Now at first seems a lot to remember but if you look closely there is a pattern. If we put write all the notes down leaving the sharps and flats we get: A, B, C, D, E, F, G. Now instead of writing in the sharp or flats in between the notes we put | instead.
So we get:
A | B C | D | E F | G | A
(if you want G string notes, start at G and work your way through the notes to G again)
Now the pattern starts to emerge, there are no notes inbetween B & C and E & F.
So we have the pattern:
A B&C D E&F G
1 | 2 | 1 | 2 | 1
and back to beginning with the | representing the notes inbetween your "regular" notes.
and that's it. So if we now look at the B string start from open string up to fret 12 and write down the notes remembering the 1 2 1 2 pattern you can't go wrong.
By simply remembering this pattern you can work out which notes have sharps or flats easily, meaning you can then know exactly what note is where on the fretboard and you can work out the notes as you play.
(This is my first lesson so hope its useful)