The V chord always wants to resolve to a I chord to our western ears.  If a V chord, like G7, resolves to its I chord (Cmaj or C-), then G7 is considered a "functioning" dominant.  Otherwise, the G7 is a "static" dominant, e.g. G7 to E7 makes G7 a static dominant.

Domininants that are "functioning" can be altered for more tension.  To alter you can:

1. flatten or raise the 5 (b5, #5)
2. add a flat or raised 9 (b9, #9)
   

Therefore, when you see a G7 followed by Amaj on a chart, that is a functioning dominant going to a I, or tonic.  In this instance, you could play G7b9#5 instead of G7.

Once these chords are "altered," you will likely want to solo over them with an "altered scale."

The altered scale (otherwise knows as the "super-locrian")  is actually the 7th mode of the Harmonic Minor scale.  It contains all the altered possibilities for an altered dominant chord -- the b9, #9, b5, #5 -- along with the root, major 3rd and flat seventh of the dominant chord.  For a G Altered scale, the notes are:

G, Ab, Bb, Cb(B), Db, Eb, F. 

This works out stepwise as:

Root,  st, T, st, T, T, T.

If you started this scale on the Ab, you would be playing the Ab melodic minor scale.  The altered scale is also known as the "super-locrian" scale, as it starts on the 7th tone of the melodic minor.  The "parent" scale of the super-locrian, is always one semi-tone above.  So to find the altered scale for F7b5#9, play notes in the Harmonic  Minor one semi-tone up from F and you will have the notes in the F altered.  

Basically, the notes of F altered and  Gb Melodic Minor are the same, which is the beauty of modes.  If you know the notes in one, you know the notes in the other.  F is one semi-tone down from Gb Melodic Minor, which makes F altered the 7th mode of Gb Melodic Minor.  That's where the "locrian" part comes in.

If you don't know the Melodic Minor,  it is essentially the major scale with a flat third.  Unlike the natural minor, the 7th in the Meldoic Minor scale is a Major 7th, only one semi-tone down from the root. 

The altered scale starts almost like the phrygian, but some things slide around in the middle.  The upper half of the scale also resembles the whole tone scale.

Here's a pdf to visualize where the altered notes are for chord construction:

Here is a link to download the pdf:

The progression of fourths is so prevalent in jazz -- just look at the 2-5-1 turnaround.  It is good to commit to memory. 

An exercise I'm going to try every day is to play the root of each note in the progression from memory on as many places on the neck as possible.  This will help with not recognition on the fretboard.  It will also get the sound of this progression in my ears.  And I will commit the progression to memory. Every day, I'll try and play it differently, with different note positions.

After I'm comfortable with that, I'm going to play the thirds of the progression.  Then the seventh of every root in the progression.  Then I'll move on from that, maybe playing the third and seventh -- our shell voicings.  Then maybe go to the sixth?  I think this will help me learn the fretboard tremendously and also get the feeling of moving in fourths to be completely instinctive.

To have total command of a song, you have to learn it in a very fundamental way.

Learn a song inside out, but one bite at a time.  Learn the melody, learn the chords.  Then find the melody on another part of the neck.  Then find the chords on another part of the neck.

The next step would be to combine the two.   Here is one way.

You can break each chord change into two sets of intervals: the root and the seven, and the fifth and the third.  This will leave two fingers to play melody.  Since each interval has one of they guidetones, you can keep the harmony very easily. 

When you bring something like an altered dominant into the mix, you can substitute a chord with contains that altered note and maybe another familiar tone... now you have two more pairs of intervals to play with: the root and seven of that chord, and the fifth and third.

Here's a youtube clip where I learned this idea.

Here is a chart of different "shell voicings" -- intervals you can use as short hand "comp" chords.  They are much faster to finger than those three and four finger chords and allow the soloist greater leeway in the harmony.

The third and seventh are the "essential tones" or "guide tones" in the changes.  Other tones can be guide tones also, like 9ths, 11ths, 13ths or even sharp or flat fives, but the third and seventh are the core of what sets each chord apart.  Since major seventh, minor seventh and dominant chords all have a root and perfect fifth, the seventh and the third are really what differentiate them.

These two notes, the third and seventh, are really "intervals" since a chord requires three tones minimum.  Since the bassist is responsible for voicing the root, the the rhythm section will fully outline the harmony for the listener. 

This chart has a range of these "shell voicings" to play.  If you have to comp for a bar of A-7, you just find an A, which is represented as the white dot.  You then find the nearest flat 3rd and flat 7th and play only those notes to comp for that bar.

Going from a 2 to a 5 is easy with these voicings.  When you move a minor seventh down a semi-tone, you will be on the third of the progression's V7 chord.  The minor third of your two voicing will turn into the minor seventh of the V7.  Just by moving one finger, you can change from a ii- to a V7.

Here is another article on shell voicings using triads: http://www.jazzguitar.be/jazz_guitar_chords_basic_shell.html

Here is a link to some flashcards to quiz you on the 3rd and 7th of maj7, mi7 and dom7 chords.

The circle of fourths/fifths is a good thing to study and learn.  Print it out and put it on your dashboard, pin it up in your cube or office at work. 

The 2-5-1 turnaround moves in fourths, which is counter-clockwise on this chart.  Many jazz songs either move in fourths or have a part of the song that does. This chart also includes the major triads which are essential to commit to memory. 

I've also included the signature for the key in the staff.  At the beginning of the staff, you will see a collection of sharps or flats (C major has no sharps or flats).  The sharps and flats are the "key signature" -- indicating the key the song is in.  For instance, if you see three sharps, that is the key of A major.  Three sharps is also the key symbol for F# minor; the companion minor of A major is F# minor.  The companion minor keys are on the inner circle of this chart.

What about those jazz hands? In a session, the leader might call out a tune and need to signal it's in E major, since songs can be played in different keys.  Since "E" sounds a lot like "B" and "C" and "D", confusion is avoided by holding fingers up for sharps and down for flats.  If a bandleader holds two fingers up, that means the song will be in the key of D major, or (B minor, if it's a minor tune).

You will notice that the number of sharps increase by one with each move clockwise and the flats increase with each move counter-clockwise until you reach the bottom.  There are two mnemonic devices to memorize how the flats and sharps progress, but guess what?  The progression also moves like the cirlce! 

The mnemonic phrase for sharps is: Fine Classical Guitarists Demand Accurate Execution (Buddy).  Congratulations, you just learned the clockwise progression of the circle!  The sharps are added in fifths.  The key of G has 1 sharp: C.  The key of D has two sharps, C and G.  The sharps keep adding as you advance.

The flats are added in fourths.  The mnemonic phrase for flats is: Be Ever Alert During Guitar Class (Forever).  The key of F has the one flat of B.  The key of B flat has the flats of B and E in the signature.  This signature adds a flat as you go counter-clockwise in the circle, advancing in fourths.  This progression is the reverse of the sharps, alphabetically.

It is wise to learn all the key signatures.  If you see a lead sheet and are uncertain, there are two tricks to help you out.  For key signatures with sharps, if you look at the note above the last sharp, that is the key.  The signature for G is the sharp of F.  Move one up from F and you get the key -- G.  For flats, the key is the second-to-last flat.  The key Ab major has four flats in the signature, B, E, A, D.  Move back one from the last flat on the signature (sitting on the D). The penultimate flat sits on the A -- therefore, the tune is in A flat.

That's all I know about the circle for now, but you can see the circle's usefulness.  This is a good reference for things to learn -- key signatures, 2-5-1 progressions, companion minors, major triads, etc.

When I first tried to learn the progression, my mnemonic was BEAD, Guitars Cause Fun.  If that doesn't stick, make up your own -- the weirder the better.  Or use "Be Ever Alert During Guitar Class Forever."  It's also good to know the alphabet starts over at F (going to flats) and F#, going to naturals.  F is for "flip" in this case.  Of course all the sharps have an identical flat and vice versa (F# is Gb), so be aware of that.