Where to Bike
VDOT publishes the official Bicycling in Virginia map. This is a good place to start if you are looking for more established routes in the central VA region. Many local parks have on or off-road paths as well. RichmondGoodLife.com has some biking-related info here.
Google Maps now offers biking directions in addition to driving, walking and public transit maps.
Try some of the Parks for starters.
Where to Buy a Bike
Laws and Regulations
The laws regulating bicycling on Virginia's public highways define the rights and duties of bicyclists as well as the motorists with whom they share the roadway. Bicyclists and motorists basically have the same rights and duties, and the laws governing traffic regulation apply equally to both. Bicyclists must obey all traffic signs, signals, lights, and markings.
VDOT has a nice summary of biking laws here. Links to the appropriate sections of the Code of Virginia are included.