If you've never been fishing before but think you might like to try, then the Virginia Department of Game and Inland Fisheries has a date for your diary. The DGIF has designated June 3 to 5 as "Free Fishing Days", meaning no fishing license will be required to cast your rod in Old Dominion waters.
The DGIF Sportsman's License, which includes a license for freshwater fishing, currently costs $120, and fishing without said license is enough to land you in some pretty hot water. So this is essentially a "try before you buy" deal, with everything except designated stocked trout waters open to the public.
If you're interested but have no idea where to fish, then cast your eyes over the DGIF's Where to Fish in Virginia guide.