In many styles of music including Country, it is common to play the bottom note of the chord, followed by the upper notes of the chord and keep alternating between them. This is known as a broken chord style of playing. The following example demonstrates a C chord played broken chord style.
Once you are comfortable playing C as a broken chord, try moving between the chords C, F and G as shown in example 7.
Here is another arrangement of Banks of the Ohio, this time using a broken chord accompaniment. Notice how the use of broken chords immediately gives the song more of a Country sound. Try using this style of accompaniment for some other songs you know.