One of the reasons we decided to hold the wedding in D.C. is because of the relative ease of traveling here from across the country (and internationally) compared with either of our hometowns.
If you're flying to the D.C. area, we'd mainly suggest using Reagan National Airport (IATA code DCA) because you can catch a Metro train into the city right from the airport. If taking a cab is more your style, a cab from the airport into the city won't break the bank, either ($10 to $15 depending on traffic). Reagan is also a beautiful airport on the inside and often shows up in movies, so it'd be neat for you to get to see it if you haven't before.
The larger and farther-out Dulles International Airport (IATA code IAD), though, has more nonstop flights to it. To get between Dulles and anywhere close to the District, you'll need to take a taxi (at least $50 to $75) or a bus (about $6). (Metrobus route 5A is popular and will drop you off in Rosslyn near the Hyatt Arlington or in a Metro station near downtown.)
Baltimore (IATA code BWI) is just a little farther away than Dulles, but there's a lot more traffic between it and the wedding venues, so the trip ends up being considerably longer/more expensive; we wouldn't recommend it. (But if you find BWI is the best option for you, you could take Metrobus route B30 and transfer to two Metro trains. MARC and Amtrak trains also operate between BWI and Union Station, but MARC doesn't run on weekends.)
Once you're in town, the Metro is probably the easiest way to get around. The ceremony and reception venues both are within a few blocks of the Metro Center station, which is on three of the system's five rail lines.
If you're a bit more adventurous about how you arrive (or just really don't like flying), you also can try taking an Amtrak train to Union Station. (It's on Metro's Red Line, which conveniently also runs through Metro Center.)
Neither of us own cars, so we might not be the best to give advice on bringing your vehicle into The District, but we do know this: Parking is ridiculously expensive, and traffic is awful. But if you are planning on driving, let one of us know so we can try to arrange parking for you at the church and reception venue, if needed.