O.K., anytime u see a chord name with a number, that number is the scale degree that has been added to the chord. So, an Ab13 is an Ab dom.7 chord with the 13th scale degree added. Here's a quick crash course in scale degrees using the key of C:
C=1
D=2
E=3
F=4
G=5
A=6
B=7
Once u reach this point u think it stops right? Wrong, it keeps going:
C=8
D=9
E=10
F=11
G=12
A=13
So, now that we know what the scale degrees are, now u need to know the basic chords:
major = 1-3-5
minor = 1-b3-5
diminished = 1-b3-b5
augmented = 1-3-#5
major 7th = 1-3-5-7
minor 7th = 1-b3-5-b7
dominant 7th = 1-3-5-b7
Those 7 chords are what I call the "foundation chords" because they are the basis for every other chord you will ever encounter. Any kind of altered chord starts with one of those 7 up there.
Now, when u get into 9ths, 11lths, 13ths, #5/b9, etc. chords all u gotta do is add the appropriate scale degree to one of those 7 "foundation" chords". So, an Ab13 chord starts with a dom. 7 chord, then the 13th scale degree is added:
Ab13 = Ab-C-(Eb)-Gb-(Bb)-(Db)-F or simply Ab-C-Gb-F
Those notes in parenthesis represent notes that are optional. That means u can play them if u want, but they are not necessary for your chord.