Instructions
Alliance
Go to Stormwind Harbor. Stormwind Harbor is located on the western side of Stormwind. If you've never been to the city before, you can travel there via the tram in Ironforge, which is located in Dun Morogh.
Walk onto the left-most boat. When you enter the harbor, you will see three boats: one on the left, one in the middle and one on the right. The boat to the left takes you to Rut'theran village.
Travel across the dock once you arrive at Rut'theran Village. Enter the pink mist emanating from under a tree to teleport to Darnassus.
Horde
Travel to Darkshore. Open your map to see the ocean in two different colors. One color is dark blue, indicating the fatigue zone, and the other area is a milky white, indicating the safe zone. Swim to the farthest point of the safe zone, which is just west of Lor'Danel.
Position your character directly northwest. Cast a water-walking spell or drink a water-walking potion. Mount up and ride northwest. Your fatigue bar should reach about halfway when you see the outlines of Rut'theran Village. You will reach land before the fatigue bar empties.
Enter the pink portal once on land to go to Darnassus.