I will explain how to read the scales by showing you an example, the Major Scale, and taking you through the steps of reading it. These Scales are written in block tab format. This means that the "tab" is used for fingering patterns, not SPECIFIC notes on the fret board.
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Ok, now each black dot is a point where you press down on the string. The bottom line is on the E string, then A, D, and G. (all in standard tuning-I am starting to like different tunings now... but that is another story) Ok, so like on the first mode (ionian) you would find a place on the E string to start. Lets start on F (first note after the open on the E string). So, the tab would be like this:


Ok, so to stay in the same key (in the same scale of course!) Lets play the second mode(Dorian)... The tab will look like this...

Notice how this corresponds to the bloc scale tab.
Ok, now hopefully, you saw something fundamental... See how the second mode starts off the first mode's second note? This goes for all the scales... The 3rd mode (phrygian)will start off the second note of the 2nd mode (5th fret)...
Ok, hopefully you got that concept... Now, since we started this scale on the 1st fret of E string, which is the note 'F'... the scale is in the KEY of F! Isn't that cool? If we started the scale on the 3rd note (after the open E) on the E string which is the note 'G' then we would play with exact same FINGER patterns starting on G and be in the KEY OF G! Here is the Tab for starting the first mode of the scale on 'G'.


The 2nd mode would look like this:


Ok, I will update real soon to add some more information to this.. This is the basics of reading the scales in block tab though.