There are three airports in the DC area: Reagan National (DCA), Dulles (IAD), and Baltimore-Washington (BWI).
Reagan National Airport (DCA)
Reagan is the closest airport to wedding events and hotels - about 15 minutes by taxi or Lyft. You can also ride the metro to downtown DC - take the blue line from National Airport Metro Station to McPherson Square.
Dulles International Airport (IAD)
Dulles is about 45 minutes by taxi or Lyft to downtown DC. You can also take the Silver Line Express Bus to the metro, and then take the silver line to the McPherson Square stop. More details on the Express Bus here: http://www.flydulles.com/iad/silver-line-express-bus-metrorail-station.
Baltimore-Washington International Airport (BWI)
BWI is about an hour by taxi or Lyft to downtown DC. Alternatively, Amtrak's Northeast Regional runs between BWI and DC's Union Station - from Union Station, you can take a taxi, Lyft, or the metro's red line to the Farragut North stop.