Learn how to get your own after the jump.
I bet you want one now, huh? Well that's cool, because I'm going to tell you exactly how to get one. Go to Org, then head up to the Bilgewater Cartel Quartermaster (he's near the flightpath) and buy the BwC Tabard. Equip your tabard, which allows you to gain rep with the gobbos in Vanilla and LK dungeons (doesn't work in BC which is intentional, not a bug), and start running dungeons! If you want this to go faster because /lfd queues are long, then while queued head up to Azshara and start questing there.
Once you hit exalted with the BwC, head back to Org and go to the goblin slums. The trike dealer can be found here:
The normal one costs 80s, and the epic one (in the screenshots) costs 8g; it's a pretty good bargain considering the source. Gratz on your new turbo trike! Unfortunately, there are only two models, instead of 3-4 skins for each as usually; that's probably because they try to keep the amount of mounts available balanced between factions, and worgen don't get one.
If you still need some convincing to start grinding your rep, here's a screenshot of the license plate, which is even cooler than the Mechano-hog's: