This app was mentioned in 2 comments, with an average of 30.50 upvotes
Learn a few major lines on the bus system. It's cheaper than metro and allows free transfers to other busses (inc Circulators)for 2 or 2.5 hrs after you first board.
The overall bus map is crazy complicated and probably scares a ton of people away, but if you just know a few lines depending on where you live and work it can be very helpful.
For example, the 30's go all the way from Friendship Heights to Naylor Rd in Anacostia, through downtown, Eastern Market and the National Mall.
Editing to add a couple of apps that will help:
DC Metro Transit - I like the interface on this one better than BusTrack DC and it includes circulator info and bus lines in PG, FFX and Arlington. It helps to already know your stop # and where you are going.
BusTrack DC - This one goes a long way to removing the intimidation factor of the busses. Just open it up and you'll see a map of where you are with bus stops. Click on a stop and see what busses are coming and when. And, if you select a particular bus from that list it will bring up a map of where it's going - very helpful if you're in unfamiliar territory.
DC Metro Transit gives real-time predictions for the Metrorail, Metro Bus, Circulator, Arlington Transit (ART), PG County - The Bus, Fairfax CUE, and UMD Shuttle.