So, I registered for the game, got my password, logged on, made my character, and now I can't leave this Civic center building on Tatooine, Help?

Try the first week Guide...

http://www.swcombine.com/guide/index.php?page=7

And be sure to read over the rest of the Guide as well.

To actually leave the building, just move from room to room until you see the option Exit. (It took me 2 days to find it, but I'm slow.)

The exit room has a different icon on the map. Since there should be only two with special icons - one being the room you started in - that should narrow down your options.