One of the first modes to learn on guitar is Mixolydian. 

I say this because after the basic major and minor, (Ionian and Aeolian), Mixolydian mode covers the third most popular chord type (the "Dominant 7th" chord) used in a large chunk of the most popular music styles; Blues, Jazz, Soul and Classic Rock... 

By learning to apply the sound of Mixolydian mode, along with it's corresponding "Major Pentatonic" scale, and it's associated arpeggio, (the Dom. 7 arpeggio), you'll be able to cover any unique appearance of the Dominant 7th chord in music.

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Practice Jam #1).
Getting solid control over the Mixolydian Mode's sound is the key to using it effectively. In our first practice jam, we'll take the color of an "A" Mixolydian mode and explore the sound of this key center with a static chord vamp that shifts between two colors of chord extensions.




The jam will move between the "A6" chord and the "A9" chord while an open 5th string "A" tone operates under the two extensions as a drone note.

Study the practice jam shown below and once you've learned how to perform the part, record it or get it into your favorite loop pedal, (I quite like the Boss RC-1 Loop Station these days, along with an old favorite of mine the TC Electronic Guitar Ditto Looper).

 PROGRESSION #1). "A Mixolydian"


Once you have recorded the above progression, start by working on melody line construction using the "A Major" Pentatonic scale. Then, slowly begin adding notes of the key of, "A Mixolydian" mode around the notes of the "A" major pentatonic. Make sure that you inject a few runs from the "A Dominant 7th Arpeggio" as well. Use the scale outline of "A Mixolydian" shown below to start working on these ideas.

NOTE: The corresponding "Arpeggio" is constructed by performing every 2nd note of the Mixolydian mode. The arpeggio tones would be "A, C#, E, G," for the "A7" arpeggio.




"A Mixolydian Scale Pattern" (6th string Tonic):


Over time, you will discover that performing scale lines and phrases that sound well connected and melodic in how they are flowing from note to note will come easier to you.

Practice Jam #2).
The next jam will be slightly more complex harmonically, plus it will introduce a few new principles of what makes up the "Mixolydian" mode color.

In Mixolydian we find a major tonality color, however it also contains a minor 7th degree. These two harmonic directions are somewhat split from each other and cause the musician some issues in trying to blend a major and minor sound off of two principle chord tones.

This is where some working knowledge of the "Dominant 7th" arpeggio comes in handy. The "Dominant 7th" arpeggio offers the entire color of the Mixolydian sound in one swoop. And, by constantly injecting the arpeggio you will find a quicker path to the "sound" of Mixolydian.





In progression two, pay particular attention to the use of the "flat 7th" degree chord (D5), and well as, the strong color of the "Minor V-Chord," (Bm7). These two chord degrees are very powerful in the world of Mixolydian and must never be ignored.

PROGRESSION #2). "E Mixolydian"
Study the practice jam below and develop the changes to a high enough level that you can record them for playback and improvisational study.



Once you have recorded the above progression, start into working on melody line construction using the "E Major" Pentatonic scale. Then, slowly begin adding notes of the key of, "E Mixolydian" mode around the notes of the "E" major pentatonic. Make sure that you inject a few runs from the "E Dominant 7th Arpeggio" as well. Use the scale outline of "E Mixolydian" shown below to start working on these ideas.

NOTE: The corresponding "Arpeggio" is constructed by performing every 2nd note of the Mixolydian mode. The arpeggio tones would be "E, G#, B, D," for the "E7" arpeggio. 

"E Mixolydian Scale Pattern" (6th string Tonic):

IMPORTANT: 
When working on both of these jams, be sure to "Compose" a lot of melodic phrases. Do not always rely only upon strict improvisation. The more that you compose ideas, the more directions you will have when it comes to your flow for natural improvisation.



CONCLUSION:
These concepts will help you with getting started with the use and the application of the Mixolydian mode. It however will take some time to master the sound and the technique of using the Mixolydian mode.

The progress that you experience will occur in bursts and as you have more success it will grow exponentially for you. Trust in your ability and always sing ideas that you hear in your head. This will allow you to tap into your will to create more and more advanced ideas.