There are three airports that service the DC area. Ronald Reagan Washington National Airport (DCA) , Thurgood Marshall Baltimore Washington International Airport (BWI), or Washington Dulles International Airport (IAD). DCA is the closest airport, but it is also the most expensive.
If you fly into DCA you may take the Metro (subway) to the Shaw/Howard University metro stop. Exit the Shaw-Howard U. Metro station in the direction of Howard University, turn right/north and proceed approximately six blocks until you have reached the main campus of Howard University. There is also a University Shuttle that will take you to the campus.
At any airport, you may also take the SuperShuttle, a van service at the airport. After retrieving your luggage, follow the signs to the Super Shuttle stop and tell them where you need to go. The cost is approximately $35 from BWI, $27 from IAD and $12 from DCA.
Washington, DC is served by Union Station. Union Station is very close to campus. A cab ride from Union Station to the University should cost between 10 and 12 dollars.
Washington, DC is served by Greyhound. They offer limited service to Union Station (the train station), which is advisable. It is much easier to get public transportation from Union Station than their First Street location, which is out of the way and can be dangerous late at night.