There are several essential country guitar techniques that if used skillfully will help you sound like an authentic country guitar player. While top country players will spend years perfecting and honing these techniques, you don't have to spend that much time to obtain an authentic country tone.
The country style techniques we'll discuss are "chicken picking," hybrid picking, hammer-ons/pull-offs, volume swells, and double-stops.
The first technique is one of the most commonly sought after country guitar solo techniques - "chicken picking." It's also commonly misunderstood. It involves muting the guitar with the heel of your picking hand - resting your hand directly on the saddles. This gives you a percussive staccato sound that sounds "plucky," hence the name "chicken picking." Some players use fingers only but many players (myself included) use a combination of pick and fingers. It helps to have a guitar like a Telecaster where you can get a real bright "twangy" sound.
If you want to play country guitar, it's really important to work on your hybrid picking, which is using your fingers in conjunction with a pick. Generally speaking, you hold your pick with your thumb and index finger and use it in conjunction with your middle and ring fingers to do everything from arpeggiate chords to do banjo-style rolls. It's an essential country technique and one you must master.
While it's not a technique that's exclusive to country guitar, you have to master really fast hammer-ons and pull-offs in order to play convincing country lead guitar. Learning how to use hammer-ons and pull-offs in time will give you a legato sound that is characteristic of many players, from Albert Lee to Brad Paisley.
One common "trick" up the country guitarist's sleeve is emulating a pedal steel sound using either your guitar's volume knob or a volume pedal. It can definitely take some practice to get this one right, but once you've got this trick under your belt, you can increase your worth to a band or add some country authenticity to your own recordings or jam sessions.
Finally, if you're going to play country guitar, you've got to learn how to use double-stops properly. A double-stop simply refers to two notes played simultaneously, and it's a great way to add some harmonic diversity to your playing. When combined with "chicken picking," it has a definitive country guitar flavor. Everyone from Jerry Reed to Brent Mason uses double-stops as an integral part of their guitar technique, so you should start learning some double-stop licks to add this technique to your vocabulary.