The Dan TELLS people the trick in one of their songs.
"C'mon man and take a piece of Mr. Parker's band!"
Their methodology starts with the study of Bird. Specirically, "Bebop" and how it changed the music world forever.
Fagen & Becker's songs are actually very simple in construct, often being a typical I, IV, V at the base level. However, the use of the harmonic extensions or even stacking triads with the so-called "pipe" chord, notated often as something like C|Bb -- which in reality is nothing more than the C11 chord, just a different way of visualizing it for the keyboard player -- can take the simple I, IV, V blues change and make it hide from you until your ears become versed in hearing the upper extensions of the chords.
Example of that is "Peg" where we have the basic I, IV, V in key of G going on through the verses. To get to where Peg happens, though, takes two devices. 1st, each chord is suspended and resolved by first playing the 4 of each chord for two beats and then rolling to the chord. Almost the same as playing the suspended 4th and resolving to the root triad, only the 5 note is also expanded to the 6th at the same time when playing it like a sus4. 2nd, they imply the Major 7 extension on each resolution, which is standard Bebop practice, whenever we see a Major chord we know that we can substitute the Major 7 or the Major 6 and get away with it if the Melody allows by not crossing the one with the other.
A very good way to start out is already given to you with that book. Get it.
But don't just simply memorize the chord changes given in that good book, although that would be the starting point, ANALYZE each song using those Roman Numerals and extension numbers. STUDY the charts in sections in an attempt to understand what's happening by simplifying things as I've tried to describe above. As you progress with that, so should your ear and the ability to recognize the same dense chording should you encounter it somewhere else.
Along with that, start learning the works of Charlie "Bird" Parker. A good first Bird tune to learn and internalixe is "Scrapple from the Apple".
Straightahead,
--Mac
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"Keep listening. Never become so self-important that you can't listen to other players. Live cleanly....Do right....You can improve as a player by improving as a person. It's a duty we owe to ourselves." --John Coltrane
"You don't know what you like, you like what you know. In order to know what you like, you have to know everything." --Branford Marsalis