Fastest way to Dalaran from 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.
Just a note on the engineering worm hole, its not random, its 5 specific places; Borean Tundra, Howling Fjord, Sholazar Basin, Icecrown, and Storm peaks from which you can choose. There is a random proc though that apparently takes you directly to the underground sewers of Dalaran, but I can't confirm that, I've never seen it happen on my device.
The Dalaran sewers portal does exist, I've seen it myself. It's useless in terms of actually getting to Dalaran though as you get locked in a small room with a vendor with engineering stuff and no way out except hearthing. With respect to the other portals, you get to choose one, but it places you in a random place in said zone. It's still quicker than taking a zeppelin though.