In Silvermoon City you need to go the Sunfury Spire, pictured in the map below (it is near at the top of the map, near the middle). The Inner Sanctum has a teleport which will take you to the Undercity.
Directly outside the Undercity are zeppelin towers, pictured below. The tower on the left in the picture will take you to Orgrimmar. There are Goblins at the front of each landing pad who will tell you which city this zeppelin is for, and where it is on its trip (intended to give you an idea of how long you'll be waiting). For example: The zeppelin for Orgrimmar has just left Orgrimmar.
If we asume you got no other transportation device then your flying mount, you'd simply jump on the "shark" Zeppelin to Borean Thundra and fly from there.
If you visit Dalaran rather often, I strongly suggest you to place your Hearthstone there, since there's a portal to Orgrimmar in Dalaran.
Other ways of getting to Dalaran; the engineering Worm Hole which allows you to chose one of a couple of randomly given zones of Northrend, which is rather close to Dalaran itself. Avoid choosing Howling Fjord and Borean Thundra since they're the most distant ones from Dalaran.
If you've grinded like a madmen with Argent Tournaments in Ice Crown, you can use their tabard to teleport there.
There's no point mentioning warlock summoning, but there's also the guild ability Have Group, Will Travel which allows someone positioned in Dalaran to summon you.
If you got silly much money and for some reason don't like to pay mages a small sum, you can on your next visit to Dalaran purchase an expensive ring which allows you to teleport to Dalaran.
I asume that you're a high level since you ask for the fastest way, and not the safiest way.
Best Answer
Take the Dark Portal to the Outland and take the portal back to Orgrimmar. It should be on your left once you arrive at the Stairway of Destiny (with your back facing the Dark Portal).