The main means of transportation from Stormwind to Darnassus is a ship and portal. From Stormwind, take a portal to Rut’theran Village. Head to the southern part of the doc where you will get on a boat that will take you across the dark shore zone and drops you at Auberdine.
Moving on, go to the southern end of that doc and get on the boat that takes you across the Eastern Kingdoms continent and drops you off at Menethil Harbor and the Wetlands.
At the front gates of Menethil Harbor, begin the long walk across the wetlands. Use the Dun Algaz tunnels to get to Loch Modan and then go through the tunnels of the North Gates Pass.
These tunnels will drop you off at Dun Morogh. Make your way across the zone to get to the Gates of the Iron Forge. Head to Tinker Town and make your way to the Deeprun Tram.
Get on the tram when it shows up. At the end of the line it will drop you off at the Dwarven district at Stormwind. Ensure to pick up flightpaths at the Gryffin Master and Thelsamar for protection.