Lake Fairfax is about a two mile walk from the nearest Metro station, so maybe 45 minutes each way. (Don't believe their web site which is outdated and states it's about ten miles. Apparently that was before they finished the latest phase of the Silver line extension.)
All the transit passes, etc. are loaded onto farecards. I think the buses also accept cash (exact change). For general touring of Washington, DC, the seven-day metrorail pass is probably the most economical and certainly the simplest to figure out. You pay about $60 up front and can take Metrorail anywhere within the system anytime its open for a week. That pretty well covers most of what you're likely to want to see in the city, especially if you're willing to do a little walking to get to e.g. the national zoo. You can get the pass (and your farecard) at the metro station from one of the vending machines there, paying either in cash or with a credit card. For your wife, you may have to figure some figures to see what plan would be the most economical. Paying per trip is a bit of an annoyance on the Metro because the fares vary with distance (starting and ending stations) and the time of day.
If you want to take a bus somewhere with the metrorail pass, you just use one of the vending machines to add the necessary fare onto the card, and then use the card to pay when getting on the bus. When I visited Washington in November for a week, the only time I took a bus was to get to the Air and Space museum annex at Dulles airport--and that was well worth the extra money and hassle to see, as it's a very impressive (and very large) collection of unique and historical aircraft.
I found the National Building Museum's free tour to be fascinating. The paid exhibits were decent, but to do again I would skip them and just take the tour.
