It bears mentioning that Reading is not about translating dots into string/fret locations. It's about recognizing musical intervals.
Reader's don't think: " That dot is A#. A# is at the 6 th fret on the E string OR 1st fret ion the A string. I choose this fret"
Readers see the musical interval between the dots and play that shape on the neck.
"the next dot is a major third away form the previous one. The shape of a major third is like this..."
Actually, I think that readers do both, but for the most part, at a subconscious level.
wcnewby, think of it like this: when you were learning written English, you first learned all of the letters and how the were pronounced. You then learned to put the letters together to form words. Later, you learned to put the words together to form sentences.
When you first started to read, it was probably a very slow process as you worked through the individual sounds you had learned for each letter, and sounded them out to figure out what word they spelled. However, as you became more familiar with the letters and the patterns that they formed, you learned to recognize entire words at a glance. You no longer needed to stop and consciously think, "ok, that letter is an r, and it has this sound, and that letter is an 'e' and it has this sound, and an 'a' has this sound, and a 'd' has this sound, and when I put them all together, they spell the word 'read.'" Instead, you looked at the four letters together and instantly recognized that they made the word "read," without ever giving conscious thought to each letter. Eventually you learned to recognize groups of words in the same way, and you were able to read whole phrases or sentences without stopping to consciously think about each word in the phrase.
Learning to read music is a similar process. At first, you have to learn where each note is on the fretboard. You also have to learn which dot represents each note. And you also have to make the connection between the dot and the fret board. With practice, those connections will become second nature so that they do not require conscious thought. Just like learning to read English, it is a process and it takes time and practice in order to become proficient.
Once you achieve that, however, you can look at a note and quickly identify where on the fretboard to play it. When you see a series of notes, you can recognize without thinking how they relate to each other in much the same way that you recognize words without thinking about the individual letters.