Get ready for a long trip! I find it best to start in Hammerfall, Arathi Highlands. Follow the road west until you see a sign that (I believe) says Wetlands-should point south. Follow road south, you will come to Thandol Span-a huge bridge. Cross this and you will be in the Wetlands. There are a few Alliance NPCs near the road to watch for, and you will eventually come to a road running east-west. Go left(east) and follow the road around the Wetlands until you come to the tunnels of Dun Algaz. There is a series of four tunnels(iirc). At the third tunnel there will be Alliance guards, level 30. For a PvE server, I'd suggest just run, you will be able to outrun them(if you attack them, it will flag you for PvP). I suppose on a PvP server it wouldn't matter, as you would be flagged now anyway(though attacking them will send out signals that you are there).
After the last tunnel you will be in Loch Modan. I always head directly east to the lake and swim south. When you come out of the lake at the southern end you will just need to go a little further south and you will be in the Badlands(noticable change in color of landscaping, green to orange!). Just inside the zone is the entrance to the instance, Uldaman-watch out for the elite dwarves working around the area). Depending on your level, avoid or fight coyotes, stealthed cats and buzzards and head west towards Kargath.