Spooky - I was about to name Old Joe Clark as an good example of a mixolydian tune.

At the risk of befuddling the enquirer, I make sense of a mixolydian tune as follows. I will use the contrast between an ordinary G major scale (which has the notes G A B C D E F# G) and a G Mixolydian scale, which has the notes G A B C D E F G.

The root note is still usually accompanied either by it's own major chord made of the 1st, 3rd and 5th notes of the scale (so in G that is a G major chord made up of the notes G,B and D). Depending on the shape of the melody, there may also be points in the tune where the root note G is also accompanied by the IV chord. In the case of G mixolydian the IV chord is still a C, just as it is in an ordinary G major scale. The notes that make up a C chord are C,E and G.

The bit that gets interesting (and can lead to enthusiastic session players playing the wrong chord) is where the melody goes to a note that in an ordinary major scale of G would want the V chord which in a G major scale is the chord of D (D, f# and A). Here, where a mixolydian melody goes to an A note, rather than accompany that with a D chord you would use an F natural chord (made of F, A and C) or a Dm chord (D F A) because these chords contain an F note rather than an F#.

I play dulcimer and getting to grips with the commonly used modes found in folk music on both sides of the Big Pond has been very good learning for me indeed!