The Mixolydian mode starts on the fifth scale degree. It is the only mode that is dominant in nature and is mostly used in blues and jazz music.
In the Key of C : C D E F G A B C the fifth scale degree is G so we have a G Mixolydian in this Key.
G Mixolydian: G A B C D E F G The intervals are therefore T T S T T S T
If we compare to G Major : G A B C D E F# G we can see that the Mixolydian mode has a b7 compared to the corresponding major scale. It is this b7 that gives the Mixolydian mode a dominant 7th nature which is why it suits blues and jazz well as they both tend to use a lot of 7th chords.
An example pattern starting on the A string is shown below. I’ve started on the A string to keep the fingering pattern fairly uniform. As with all the modes, you definitely want to experiment a lot with playing this pattern in as many different positions as possible (audio here):
If you need a diagram showing the notes on the fretboard, one is available in the Ionian mode (Major scale) post.
The first example is played over a C7 chord (audio here).
The second example uses a G7 G7 Dm Dm C7 C7 (V7 ii I7) chord progression which has the Mixolydian mode played over the top of it as shown below (audio here).
These are fairly simple examples to get you started, hopefully you can hear the blues / jazz sound of this mode. Good luck, and the most important thing – have fun!