The easiest way would be to go east through Ashenvale until you get in to Darkshore. Make sure to stay off the roads as much as possible, or you'll end up running into Astraanar (Alliance town). In Darkshore, run all the way up the coast until you get to the Alliance town there, and get into the water. Swim all the way to the very end of the dock, where a boat docks. This leads to Azuremyst Isle. Drown somewhere underneath where the boat stops. While you're a spirit, run ON the dock to where your body is and wait for the boat. Get on it, and when the boat hits the loading screen, it'll resurrect you.
If you die to an alliance NPC, make sure that you at least try to die OFF the boat, so you can run back to your corpse, or else you'll end up back in darkshore.
Also, make sure that you have Burning Crusade installed. If you don't, you can't get to the island.