Please note that Geb is primarily a developer tool. You'll need to be comfortable coding and debugging automated tests as a developer would.
Does your team already have an existing suite of Geb tests?
In the past, I've had a couple successful geb experiences where QA resources wrote & ran test suites. I think this was successful because the developers on the team had already built up page objects and established patterns & helper methods that could be extrapolated on. Basically we built the framework that the QA team members would utilize. Beyond that it was helpful to have a developer on hand who could help decipher any weird issues.
You'll need to be familiar with Groovy and will end up needing to know a little about WebDriver. I don't know of any tutorials but as Marcin & Brian pointed out there are are a couple good resources to get started with: