Yes after you talk to the Baderon at the Limsa Lomisa, the Seaside city, you must take the ferry to Aledor i think it is called, and find the cavern outside of the city, just to the north. There you HAVE to talk to the NPC waiting there, and that triggers your being able to click on the swirly in side the entrance area to register for the queue for the start of the Dungeon. Be sure to leave "Join Party Already in Progress" unchecked unless you want to be thrown into an already existing party when someone quits, it can take forever and i checked it at first without knowing what it meant. Let us know if you got in, once you do this one you will be able to get others.

This first dungeon has a good tutorial set of screens be sure to look at them all or you will not find them saved in your log.