Quick run down.....

Market Wards is the "Auction House". (In ul'dah i believe its called "The Dunes" on the map)

Use the item search and check through the various wards to find what you need. A red star appears above the retainer that holds the item you are looking to purchase.

There is no mail delivery system as of now, so either have a LS friend help you transfer stuff to a mule or you can chance it and put it up in a retainer in a ward and then log on other character and buy that item from the said retainer. Its tricky but can be done.