This is how to get from the Human city of Stormwind to the Neutral city of Booty Bay in Stranglethorn Vale at the southern tip of the Eastern Kingdoms:
Teleport via Gleep Chatterswitch
Considered to be the quickest way in general, as of patch 5.3.0. On the Summer Terrace at the Shrine of Seven Starsyou will find a Gnome NPC, Gleep Chatterswitch, who will teleport you to Ratchet via his Goblin Teleporter for ten gold. Pay Gleep the gold and step into the Teleporter. The port will land you on a dock in Ratchet, from that dock take the next ship to Booty Bay.
Run through Darkshire and Stranglethorn Vale
There's a dangerous path straight south through Stranglethorn Vale you can take:
Either fly from Stormwind to the town of Darkshire in Duskwood or run southeast to get there (you can safely do this around level 20). You can also follow the road south from the Redridge Mountains.
Follow the road south from Darkshire and turn west with the road.
Keep going west until you get to a road going south (at the intersection should be a tent with Darkshire watchers) and go south.
The road south leads into Stranglethorn Vale. For characters under level 30, this area can be scary, so be wary ofmobs. You may die a few times.
There's an alliance flight path right when you get to Stranglethorn Vale. Cross the first bridge (over a dry gully), follow the road, and head west at the first intersection. The flight path is in the Rebel Camp subzone.
Follow the winding road generally south over a couple of rope bridges past the Venture Trading Company Base Camp and continue south.
You should pass the Gurubashi Arena and eventually get to a large shark head at the opening of a cave guarded byGoblin bruiser guards.
Go through the cave tunnel and you've made it to Booty Bay!
If you are a lowbie, and die along the way, you can't keep running as a ghost until you get to the cave right outside Booty Bay. Although there is a Spirit Healer just slightly east of the cave entrance, you can't resurrect from there and run right inside Booty Bay, because if you try to resurrect at a different Spirit Healer, it will resurrect you back at the graveyard you died at.
Swim from Westfall
Another way to get to Booty Bay from Stormwind is to start from Westfall. This method is recommended for lowbies (lvls 10-19) since it is the safest.
Fly to Sentinel Hill in Westfall, then run southwest until you reach the southern coastline of Westfall.
Proceed to swim south towards Booty Bay. Stranglethorn Vale's western coast is quite generous in how far you can stray away from shore without being fatigued, so you can swim in an almost straight line. Note that this takes about twenty minutes.
Stay away from the shoreline, you don't want to aggro mobs or alert Horde players at Grom'Gol!
When you reach Booty Bay's harbor there is a ramp in the center of the dockside that will allow you to get out from the water.
Welcome to Booty Bay!
Along the coast of Theramore Island
Another, both relatively quick and rather safe - way to get to Booty Bay from Stormwind or other Alliance territories is to take the roundabout route via Kalimdor.
Start in Menethil Harbor (fly there, or walk the long way; pick up the flight path if you do not have it).
Take the boat to Theramore Island
Head north along the beach to Ratchet. There are some level 37-38 Murlocs in the way, but you can completely avoid them by swimming east around Island Alcaz. Closer to Ratchet are some level 13-16 pirates, but they too are easily avoided. If you die to the pirates you will resurrect directly at Ratchet. It should be mentioned that along the beach there are various Defias mobs, all ranging from 37-38. Simply swimming in the water will not avoid them, either, because Defias Divers (also 37-38) are almost unavoidable. Swimming east around Alcaz is the best route.
From Ratchet, take the boat to Booty Bay.
If you take this route, you also get the flight paths in Theramore Island and Ratchet as a bonus - don't forget to pick them up!
Ashenvale to Ratchet
For a character close to level 20, this might be the best way. (The swim from Westfall is not hard, but it is tedious.)
This is especially useful if you are already in Silverwing Grove buying Warsong Gulch PvP reward gear from Illiyana Moonblaze.
Take the boat from Stormwind to Auberdine on Darkshore.
Follow the road south from Auberdine through Astranaar in Ashenvale.
Keep going east along the road, past the sign for Raynewood Retreat.
After you cross a bridge spanning a river, turn south on the road toward the Barrens, which passes Silverwing Outpost.
As you approach the Mor'shan Rampart head east off the road. You will see a gap in the wall which is safe and has no guards.
Go through the gap and keep heading south. Ratchet is southeast of your entry into the Barrens.
Paralleling the road works, but stay clear of Horde guard towers, and skirt around Crossroads.
Take the road southeast from the Crossroads to Ratchet.
Another option for crossing the Barrens to Ratchet is to go through The Sludge Fen east to the Southfury River.
Then follow the Southfury River south to Ratchet, avoiding the Horde guards at the bridge across the Southfury River.