I'm pretty sure you'll need your own transport to reach Virginia City. There may be tour buses, but I never saw any! Once you get there, the parking is free. Park on the right side, just as you enter the town. You can also park down by St Mary's Church.
Virginia City is 23 miles from Reno. South on Hwy 395 for 10 miles, left on Hwy 341 for 13 miles.
From Carson City it's 14 miles. East on Hwy 50 for 7 miles, then left on Hwy 341 for 7 miles.
From lake Tahoe it's 40 miles. East on Hwy 50 to Carson City, then as above.
Virginia City lies in extreme western Nevada at the base of the Sierra Nevada Mountains, just south of Reno and Interstate 80. It lies along scenic route SR 341 between U.S. Route 50 in Carson and U.S. 395.
Virginia City is about 45 minutes from Reno. Your best bet getting there is a car. I don't know of any buses that will take tourists there.
THe city itself is rather small so you should be able to walk almost anywhere in town.