I teach it like a maths thing; four main numbers to remember...12, 7, 5 and 2. Then learn the 12 notes on the bottom E string and for now, do away with either the flats or the sharps; it's hard enough learning one than trying to remember two!
So therefore the notes from open to 12th fret are:
E F F# G G# A A# B C C# D D# E
(13 notes here because we repeated the E)
Make the very early distinction regarding the E-F and B-C that there's no sharp (or flat) between these notes. If you look at a piano you'll see that there are no black notes between them. Come up with a short sentence like 'Every Friday Buy Coke' or whatever to get that EFBC thing in your head.
Then look at the 5th fret on the E...you tune the A string to this right? That's because it too is an A. So you've made the discovery that you are only maybe 5 frets away from the same note on the next string down. This is where the number 5 is important. The 6th fret on the bottom E is A#...so is the 1st fret on the A string...there's your 5 note gap.
So you can start from the bottom E and when you get to the A on the 5th fret, start to count from the 1st fret on the A. If you count up 7 frets, you'll again come to an E...because 12 in a row is the same as 5 and 7 ain't it?!
Now do the same on the A string...5th fret is a D. You know this because you tune the D string to get the same note. Start on the 1st fret of this string and the 2nd fret is E...because 5 + 5 + 2 also = 12!!! Now you're starting to see all the E's. So open 6th string, 12 fret 6th string, 7th fret A string, 2nd fret D string...see how it's going?
As mentioned before you can also do the two strings across and two frets up but make sure you add another note and go up 3 frets when you're going THRU the B string...not just when you are ON it...you've lost a fret because of the tuning and as soon as you go thru the B you have to add that note. Very soon you'll look at the neck and see that it really is only 12's, 7's, 5's, and 2's (with the odd 3 thrown in because of the tuning). Then it ain't so scary.
Fretboard Warrior is great also to get this in your head. If you don't know the note, go down two and across two (or three when over B) until you see a note that is familiar. Also look at the coralation between the open, 5th 7th and 12th fret. They are obviously both the same (EADGBE) on the open and 12th because that's the natural octave. BUT look at the 5th fret and you get ADGBEA (4th fret on the 3rd for the B) and the 7th fret is BEADGB (8th fret on the B for the D) and you see that all the note names are the same just starting further along. Of course because of the bloody tuning of the B, you have to remember to move accordingly but, on the whole 5 out of the 6 strings are easy enough to remember and you will eventually get used to it.
I know it was long-winded but take a bit of time and you'll see it makes sense! Also www.fretboardwarrior.com for naming note games! ;)