If you've got a little time, someone has started a "Let's Play" video series (link in text) that walks through stuff for beginners. You might want to check that out.

You'll probably want to head the Adventurer's Guild first. There's a different one in each city. It will give you some quick tutorial-like tasks that will introduce you to some basic concepts.

Then go to the leve desk. It's in the Adventurer's Guild. It's the place with the big green windows over the top of it, and it's represented by a blue-ish window thingy on your mini-map. Talk to the two folks behind the desk there. One will offer you Battle Quests. Since you're just starting out, I'd suggest starting with the tutorial quests. Then you'll have to head to your first camp. They're very easy, so feel free to run them on 2 or 3 stars.

Like Poppa said, I'd suggest joining a LS. But I don't think you need to wait until level 20 to do it. I'd suggest joining one as soon as possible. Consider checking out the forum for your specific server here, or shouting in Uldah for a LS. It's just a lot more fun to play with other people, and it's also a lot easier when someone else can help explain stuff to you.

Have fun!