Your best bet is to use the Metro station (DC's version of a subway, although much of it outside of DC runs above ground) at Franconia Springfield, which also happens to be very close to the Springfield Mall. It's a 15-20 minute drive from Fort Belvoir. The Huntington Stations is also an option--some would probably prefer Huntington but I think Franconia-Springfield would be easier for you.
If you're going to park at a Metro Station, you have to pay for parking during the week--and that's a real pain in the butt for visitors. The reason is you have to have something called a "SmartCard" to get out of the garage. You can get a Smart Card at any station--they allow you to add value by putting cash in the machine and touching your card to it. You can also use a credit card. The SmartCard itself costs $5.00--and then you need to add enough value for your fare and your parking. To give you an idea, parking during the week costs about $4.50 at the Franconia-Springfield Station. The rush hour fare from Franconia-Springfield to downtown DC is $4.35. Off-rush hour (weekends, the middle of the weekday, and evenings) is about $2.35. The trip from Franconia-Springfield takes about 40 minutes. Trains leave about every 6 minutes during rush hour and about every 12 minutes otherwise.
One advantage of Franconia-Springfield is that you can park at the Springfield Mall for free and then walk (a little more than one quarter of a mile) to the station.
There is bus service from Fort Belvoir (the Richmond Highway Express Line) that will take you to the Metro Station.
You can get more information on options at the Washington Metropolitan Area Transit Authority (WMATA) website: http://www.wmata.com/default.cfm
Fort Belovir is in Fairfax County and Fairfax County has a couple of other public transportation options--most notably the Fairfax Connector bus service. Web site is here: http://www.fairfaxcounty.gov/connector/
Alexandria, Virginia has a DASH bus service. You're less likely to find this useful unless you plan to sped some time in and around Alexandria (not a bad idea, by the way--Alexandria's Old Town area, near the King Street Metro, can be fun). Web site: http://www.dashbus.com/