One of the most common ways swing 8th notes are used in Country music is as a shuffle. The term "shuffle" means a constant stream of swinging 8th notes. Here is the shuffle rhythm applied to a typical left hand pattern. It should sound familiar.
Here is a common Western Swing accompaniment pattern. In this example, the shuffle effect is created by both hands, with the left hand playing on the beat and the right hand playing off the beat.
This one features another common left hand pattern which has been used in many styles of music. If you have trouble coordinating the hands, practice each part separately at first and count out loud as you play.