If you're not sure which Zeppelin on a platform is which, you can talk to the Zeppelin Master on the platform and they will mention which city they serve.
Although it is hard, players of the opposite faction may board a horde zeppelin. Be prepared to battle the crew and guards stationed there.
At Orgrimmar, the Zeppelin Tower on the plateau (just north of the flight master) in the center of Orgrimmar(before Cataclysm there used to be a docking tower outside Orgrimmar in Durotar). The one that leaves from the west edge of the tower will take you to the Undercity; the east side goes to Grom'gol in Stranglethorn Vale. In Wrath of the Lich King, another tower was added that flies to Warsong Hold in Borean Tundra, Northrend. The tower's south side takes you to Thunder Bluff. (This is helpful to lower level Tauren players allowing them direct access to Orgrimmar without the need for the Barrens run.)
At Undercity, the Zeppelin Tower is just north of the entrance to the city. The one that leaves from the west edge of the tower will take you to Orgrimmar; the east side goes to Grom'gol. In Wrath of the Lich King, another tower was added that flies to Vengeance Landing in Howling Fjord, Northrend on the north side.
At Thunder Bluff the Zeppelin Master Krendle Bigpockets is located on the west of The Spirit Rise(19.2, 25.6) which takes Tauren players directly to Orgrimmar.
At Grom'gol Base Camp, the Zeppelin Tower is inside the outpost and doubles as the inn. When on top of the tower, the side that faces over the water will take you to Orgrimmar, while the other side will take you to Undercity.
There is a boat connecting The Barrens in Kalimdor and Stranglethorn Vale in the east. The boat docks at Ratchetand Booty Bay, respectively.
Boats and Zeppelins remain docked for exactly 60 seconds before they move on. The exception is the Feathermoon Ferry, which docks for exactly 30 seconds.
Each boat and Zeppelin keeps its own precise schedule, but each has a slightly different cycle in the 3 to 5 minute range. For example, Undercity-Orgrimmar runs every 3:59 while Undercity-Grom'gol runs every 5:15. Using the addon Nauticus can make timing your travels easier, since it shows arrival and departure times of any boat or Zeppelin that you (or anyone else on your realm running the addon) have used at least once before.