Train/Public Transportation
Columbia is known as a working suburb of both Washington, D.C. and Baltimore, and therefore there are relatively close stations near the city that connect to the Amtrak network into D.C.'s Union Station and through Baltimore and Baltimore's light-rail network. BWI Rail Station is the closest Amtrak station, a stop for express trains on the Northeast Corridor route. Catch the light-rail at BWI.
Howard Transit offers hourly bus service on its Silver route from the Mall in Columbia Town Center to BWI and the rail station. At the airport, catch the Silver route bus outside Pier E, the International Terminal, on the lower level.
Columbia is not convenient to the Washington, D.C. Metro system, with the closest stop being Greenbelt in Prince George's County. MTA Maryland commuter bus routes connect Columbia to Washington and Baltimore, but these services are intended for transporting workers to jobs, and run only on weekdays early in the morning and late in the evening.
Car
Columbia is easily accessible off the main I-95 north-south interstate. From I-95, take either Route 32 West, Route 175 West, or Route 100 West into the heart of Columbia Route 175, which changes its name in Columbia to Little Patuxent Parkway, will lead you to the city center and the Mall in Columbia -- the primary shopping/activity area.
Coming from the West i.e. Frederick, MD, take I-70 East to US-29 South. US-29 cuts through the heart of the city and will have the same exits as I-95, namely Route 100, Route 175, and Route 32.
Air
Columbia is served by BWI - Baltimore Washington International - Airport. The airport is a major hub for budget carrier Southwest Airlines, and as such has a large network of connecting flights to almost every major U.S. city, in addition to its own international terminal and connecting flights to larger international hubs such as New York's JFK and Atlanta's Hartsfield-Jackson International Airport.