The link provided by 10 Wheels - http://www.atatrail.org/ - will cover the stretch from near Pittsburgh to Cumberland, Md. The stretch between Cumberland and Washington, DC, is the C&O Canal and is covered by this link: http://www.nps.gov/choh/index.htm . I strongly suggest gettings maps and brochures from both websites.

I've ridden parts of both. The GAP Trail is a nice hard-packed trail with several nice small towns along the way ... very well-maintained. The C&O Canal trail is more remote in some places and not as well-maintained in general. There are some parts that are pretty rough.

I think just about anytime between April/May and September/October could work. In the higher elevations along the GAP, you might have to deal with cold temperatures and snow in early April or late October. Also along the GAP, there are a few towns that are popular tourist/"adventure" draws during the summer months so plan accordingly. I actually had a trip planned along most of the GAP for the first weekend in November - just a couple of months ago - that we had to cancel due to snow.