Steps to Serving in the Georgia Republican Party 2011 (opens a PDF file)
Your precinct will be your Georgia State Senatorial district. Not sure what yours is? Visit the Georgia Secretary of State's My Voter Page and input your info. You will need to contact your county party office to find the meeting location. That information is published in local newspapers, but can be hard to find.
If you are interested in getting involved in county or state party organizations, the Georgia GOP Events page is a good place to start.