The best way to getting to Killington from Washington DC depends on your budget. The Amtrak to Rutland or White River Junction goes via NYC and it's very affordable but very slow. Flying would be quicker and you cna do so by taking Jet Blue to Burlington via JFK or go to Manchester NH or Bradley CT.
I would recommend Amtrak instead of driving because the drive is kinda tiring and you never know what the road conditions will be. There's only 1 Ethan Allen Express daily from NYC Penn Station to Rutland, which is the closest train station to Killington. Once you get to Rutland, you can a taxi or the Diamond Express bus (only $3) to Killington.
It's surprisingly cheap to take [b]http://www.destination360.com/travel/amtrak[/b] if you plan ahead. There are a number of discounted seats available on each trip, so it can be much, much cheaper than flying. Plus, it might even be low enough to be cheaper than driving.