From I-95 take Exit 30 towards Augusta, then turn right across from the Armory (the 2nd light? It's just before Shaw's shopping center and a Burger King).  Follow that road around the corner to the left and down over the hill.

You can park in the parking garage on the left - turn left at the light at the bottom of the big hill (Sewell St) and then right into the parking garage. You can go into the Cross State Office Building across from the parking garage - there's a connector in the middle of the building leading to the State House main entrance.