Learn basic chords on the instrument of your choice. It doesn't matter whether you play piano or guitar. Western music often features basic chords and simple rhythms that sound good on an acoustic guitar or piano, which makes western music one of the easiest genres for a beginning musician to accomplish. C, D, E minor, A and F chords are good to begin with.
Start with an early classic folk song such as "Oh, Susanna." The chords are simple, it's easy to strum, and it can help prepare you for playing some of your favorite country and western songs. You can find "Oh Susanna" and other early western songs online at no charge (see resources).
Listen to some of your favorite western songs. Listen for the rhythm of the song and try to replicate the rhythm on your guitar or piano. Typically, when you're playing a western song for fun, a simple up and down strum pattern will work on a guitar and a bass note/chord pattern on the piano.
Sing along if you can. Practice as many of your favorite songs as you can find. The more you practice, the better you will get. Singing along to songs you're familiar with will help you play your song in time and can make playing the song more enjoyable.