You would normally accompany it with major chords, but with an occasional chord which is a tone below the tonic. In other words, if you are in D major, expect to play an occasional C major chord; if you are in G, expect to play an occasional F chord and so on.

Myxolidian tunes that you might know - Blackwaterside, Sullivan's John, Norwegian Wood, Dark Girl dressed in blue (polka).

Does that help?

Tradsinger