Choose a key to practice in; C is a good start. Strum the first and fifth major chords in the key of C. These chords are C major and G major. You can play a simple western swing on these two chords that demonstrates the sound and feel of the style.
Establish a 2/4 time signature. In music, the time signature tells you how many beats there are per measure of music. To play a 4/4 time signature, you would play four beats per measure, with the accented count typically coming on the first and third beats. In 2/4, also known as "cut time" or "half time," there are two beats per measure, with the accented beat on one. This gives western swing its quicker, boppy feel. Count, "One and two and, one and two and," in your head. Strum the C chord on the first "one and two and," then strum the G chord on the second "one and two and." This is two measures of western swing rhythm. Strum them several times, strumming down on the count and up on the word "and."
Once you have established the rhythm, add walking bass to the chord pattern. Walking bass is a short run of notes played on the lower strings of the guitar while you continue to strum the full chords. On the C major chord, pick the lowest note of the chord (third fret on the fifth string) on the count of "one" and strum the chord on the "and." Do this for two full measures, then switch to the G chord by playing a descending single-note pattern of third fret to the second fret on the fifth string. Play these two notes with the same rhythm you've been using to strum the chords, with the third fret on the "one" and the second fret coming on the "and."
Approach the G major chord on the "two" count after the single notes. Play the low note of the G chord (third fret, sixth string) on the count of "two" and the full chord on the "and." Practice playing these patterns at a steady, uptempo pace and you'll be playing a steady 2/4 western swing in no time.