Nothing in climbing is more important than belaying. Belayer's hold their partner's life. While many people are cavalier about belaying, it's an essential to pay attention and belay properly. They are significant differences in belaying a sport route, a long traditional climb, or an aid climb. The single most important tenet of belaying is to never let go with the brake hand.
Belaying well involves more than just holding the rope for your partner. Using an ATC or GriGri requires a significant amount of attention to the activity of the climber. It's important to pull in and feed out rope at the correct times. In this instructional video, Adam Barczack demonstrates the proper way to belay.
Even with an autolocking device like a GriGri, it is essential to hold on to the rope. Keep your brake hand close to your body to avoid letting go of the rope. Make sure to establish a set of commands before leaving the ground. The climber's knot should be tied perfectly and the belay device needs to be locked and properly loaded. Also, keep your eyes on the climber at all times.
The Touchstone Gyms offer solid instruction on how to belay. Ask the front desk staff for more information.