This lesson will be about common jazz chords, how they are written, and common ways to play them. And common practices to sightread them. I highly recommend reading my other lesson, "Identifying Intervals", I use a lot of that information in this lesson.
The Dominant Seventh.
The dominant 7th chord is the most used chord in jazz. A dominant seven is a flatted 7th. A dominant 7th chord consists of the Root note, the Major 3rd, an optional 5th, and the dominant 7th. A Dominant (or minor 7th). 7th can be identified when you have a note on the same fret, two strings above. It is sometimes called a "Major Minor" chord.
C7
|--8---------|
|--8-----5---|
|--9--3--3---|
|--8--2--5---|
|--10-3--3---|
|--8---------|
Cmaj7
|--8-----3---|
|--8-----5---|
|--9--4--4---|
|--9--2--5---|
|--10-3--3---|
|--8---------|
Cm7
|------------8--|
|--8---4-----8--|
|--8---3--3--8--|
|--8---5--1--8--|
|------3--3-----|
|--8------------|
C9
|------------|
|-----3------|
|--7--3------|
|--8--2------|
|--7--3------|
|--8---------|
Cm9
|--10--------|
|--8---3-----|
|--7---3-----|
|--8---1-----|
|--10--3-----|
|--8---------|
Cm7(b5)
|------------|
|------4-----|
|--8---3-----|
|--8---4-----|
|--9---3-----|
|--8---------|
Cdim
|---------8--|
|------4--7--|
|--8---2--8--|
|--7---4--7--|
|--9---3-----|
|--8---------|
C13
|------5------|
|--10--5------|
|--9---3------|
|--8---5------|
|------3------|
|--8----------|
C6
|-----5------|
|--8--5------|
|--9--5------|
|--7--5------|
|--7--3------|
|--8---------|
Cm(maj7)
|-8---3-------|
|-8---4-------|
|-8---4-------|
|-9---5-------|
|-10--3-------|
|-8-----------|
Altered Bass Chords.
Altered bass chords are also self explanatory. Most of the time, guitarists do not have to worry about them because it usually means the bass is hitting the note. Basically, in an altered bass chord, it is signified with a slash, with another note next to it which should be in the bass. Same thing with these go with altered chords, you have to figure out the voicings yourself because there are just to many to cover in a lesson.
Okay, so you got all this down, but you still can't keep up in your jazz band with the chords because you don't have them all "memorized". Well, all you really need to know is how to form most of these shapes, and move them around on the neck. All of these chords are movable. They are all different forms of C chords, of you move them all up a whole step, they will become different forms of D chords. That should be simple. So, all you really need to do is find your fifth and sixth string roots of the chords, and place the root note on the correct note.
My words of advice: you don't need to memorize the entire fretboard for this, I'd just get extremely familiar with the 6th and 5th strings, where most of these chords should be played. It's bad to play a 6th string root F chord, because it's so close to the nut and not all the notes are clear as you'd like them to be. It's also not the best idea to play a 5th string root G, because that’s really high up there and the guitar will stick out a lot more than you'd like it too in a combo. A comfortable spot to play these chords is from a 6th string G and the 5th string G. (in standard tuning, of course).
When looking at a piece of sheet music with chords on it. The most common strumming pattern would be to follow a "2 and 4" type pattern, accent the second, and fourth beats, and hit the bass note on 1 and 3. Hitting the bass note on 1 will give you an extra beat to get your fingers ready for the rest of the chord.
It takes a long time to get used to sightreading chords like this, I still have trouble myself. When I first started in a high school jazz band, I was completely lost, nobody to help me. I learned that the easiest way I could sightread was to play powerchords on the root of the chord being played. This got me familiar with the 5th and 6th string notes and how jazz patterns usually move. Although this sounded really really really bad in the music, it was start and helped me down the line with fluency. Then I played the basic bar chords after I could comprehend dominant, major, and minor 7 chords. This is fine if you can play it like this. It is a really good thing to leave out the 5 of the chords, because it only makes chords more filled out, which isn't really jazzy in my opinion, which is the only part of bar chords I don't like. Once you get used to the voicings that do not require the fifth, you will notice the difference.
It takes a lot of time, practice, experience, and the will to learn in order to become a fluent chord reader. Do not expect to get these as you read them. Print them out, look over a page in "The Real Book" or any other sheet of music, look through it, practice sightreading over it, and go to the next one, and repeat.