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PvE Servers
For those of you on non-PvP servers, you can use the route from the Night Elf town of Rut'theran Village, fly to Lor'danel,Darkshore and on to Neutral city of Booty Bay at the southern tip of the Eastern Kingdoms:
Either fly from Rut'theran Village to Lor'danel and on to the town of Astranaar in Ashenvale or follow the road south to get there (you can safely do this around level 20).
Follow the road east from Astranaar until it forks south towards the Northern Barrens.
Follow the south road until you get near entrance to the Northern Barrens.
There should be a break in a fence to the east of the guard tower. Go through it, making sure to avoid coming near the guard tower.
Travel southeast to the Neutral city of Ratchet, along the coast, making sure to avoid Crossroads.
Jump on the Booty Bay boat at the Ratchet dock.
PvP Servers
For those of you on PvP servers, the following route is usually less crowded, and may thus be easier to follow:
From Rut'theran Village, take the boat to Menethil Harbor, then from take the boat to Theramore Isle.
Head north along the beach through a short part of the Southern Barrens to Ratchet. There are some level 37-38Murlocs in the way, but you can avoid them by swimming around them. The mobs around Northwatch Hold used to be lightweight at around level 13-17, but now they should be friendly Alliance level 28 - 33. You might want to pickup the flight path at Northwatch Hold while you're passing through.