Just for your information, there was a boat from Auberdine in Darkshore to Rut’theran village at the base of Teldrassil, but that was a long time ago. Ever since the Cataclysm expansion launched in 2010, that ferry is no more and the port city of Auberdine is ruined, so you’ve probably been watching a few old videos.
The way to get to Darnassus now, is to talk to the timewalking NPC, and then go the northern coast town of Lor’Danel. There you’ll find a flight master on top of some wooden scaffolding jutting out into the water from where you can get a ride to Rut’theran village at the base of Teldrassil. Once in Rut’theran, walk through the glowing purple tree to be teleported to the city of Darnassus.
The same flight master in Lor’Danel will also give you an option to fly directly to Darnassus, but the flight up the tree takes a long time (4 minutes or so iirc), so I advise you to just get a ride to Rut’theran and walk through the portal tree there.