The Georgia State Capitol building is only one block away from the Georgia State MARTA Station on the blue/green rail line. The building is open to the public Monday-Friday from 8 a.m. to 5 p.m., and is closed on weekends and holidays. Visit website for tour information.
If you are coming from the red or gold rail line, exit at the Five Points Station and follow the signs to the Eastbound platform. Get on the first eastbound train and ride one stop to the Georgia State Station. Take the Piedmont Avenue exit out of the station and turn left on Piedmont Avenue. Walking time is less than 10 minutes. Nearby destinations include Underground Atlanta and Georgia State University.
For more information, see:
Navigating the Georgia State Station
10 Popular Atlanta Tourists Attractions and How to Get There on MARTA