Belaying a leader in a climbing gym with a Gri-Gri requires some skills you won't have learned if you've only belayed with ATC-type devices. Luckily it's not hard to make the adjustment.
For an overview, check the Petzl technical page: Belaying with the GRIGRI
The big thing to learn is how to momentarily allow rope to be pulled through the GRIGRI without blocking the cam's action.
- Hold the rope with at least three fingers.
- Use the index finger to support the GRIGRI
- The thumb presses on the cam.
The action must be momentary, and as soon as the leader has clipped return to the primary belaying position.
More of a visual learner? Have a look at the official Petzl video.