First of all, I hope I didn't offend anyone with my "theses" remark--I was just commenting on how in depth some of the answers were...a far cry from some of the usual soundbyte wisdom that gets spouted when somebody asks this question.
There's really not one way to come at jazz, but there are a few things you absolutely need to have down if you're going to get anywhere with jazz guitar...I call 'em the "non negotiables."
You can know these things academically or intuitively...preferable both, IMHO. If you're going to rely on one or the other, you had better REALLY know it. Very few people can play jazz on intuition alone...this is why I always fly off the handle when someody says, "well, Wes Montgomery couldn't read music..." I usually say, fine, when you can find your way around the guitar like Wes, feel free to not read music.
Anyway, here's the non negotiables:
The major scale in every key. Know it, be able to play a major scale starting on any note on the guitar...put a finger down, play a major scale up and back down from there.
Chords...at a bare minimum, maj7, m7, 7, m7b5, and a few jucier #'s like 9ths, 11th, 13thss, etc. You need a couple of dominants with alterations--gotta know 7b9, 7#9, 7b5, 7#5. Oh, and you gotta know at least three places to play those chords--- one with the root on the sixth string, one with the root on the fifth, one with the root on the fourth string. Eventually, learn their inversions too. Learn arpeggios for those chords as well.
And then you have to listen...jazz has to be the music that plays in your head all day every day...If you can't hear it in your head, you can't play it.