Planes, Trains, and Automobiles
Washington DC is served by three airports, Reagan National (DCA), Dulles International (IAD) and Baltimore-Washington International (BWI).
Reagan National Airport is the closest option, located across the Potomac River between Alexandria and Arlington in Virginia. DC's metro is the most efficient way to get from DCA to the Folger. Simply hop on the Yellow Line toward Fort Totten, switch to the Blue or Orange Line toward Largo Town Center or New Carrollton at L'Enfant Plaza, and exit the metro at the Capitol South station. The Folger is located one block east and two blocks north at 201 East Capitol Street, SE. Taxi cabs are the slightly more expensive option, at between $15 and $20, one-way.
Dulles International Airport is a bit further afield in Northern Virginia, located in Western Fairfax county. The best way to commute from Dulles is to reserve yourself a seat in the SuperShuttle ($29, one-way). Taxi cabs are the more expensive option, at between $60 and $70 one-way.
Baltimore-Washington Airport is located just south of Baltimore, Maryland. If you're visiting the Folger during the week, catch the free shuttle from the airport to the Thurgood Marshall train station, and Maryland's MARC commuter train will take you straight to Washington, DC's Union Station ($7, one-way). If you're traveling on the weekend, when the MARC train does not run, you can purchase a ticket from Amtrak to get you to and from the airport ($14, one-way). Taxi cabs are the most expensive option at between $65 and $75, one-way.
DC's train station, Union Station, is located 10-15 minutes from the Folger and is a stopping point for many modes of transportation: the metro, MARC, Amtrak, and the Virginia Railway Express (VRE).
A note about driving: As is the case in any city, parking comes at a premium in DC, and this is especially the case on Capitol Hill. The Folger has no parking to offer visitors or readers. On-street parking in the neighborhood around the Library includes metered parking and time-limited parking. Meters have a maximum of two hours; you cannot avoid a ticket by feeding the meter all day. Time-limited parking is also restricted to two-hour stays; moving your car after two hours to another space in the same residential parking zone can still result in a ticket.
Luckily, Union Station also has a multi-tiered garage and is available 24/7. The cost for 24 hour parking is $22.