Pick up the the St. Charles streetcar (Green Line) at Canal Street and Carondelet. (You'll see the sign by the curb, "Street Car Stops Here." You can also pick it up along St. Charles, but chances are that you won't get a seat. The line begins at Canal and Carondelet, and we had our pick of seats when we got on.) Take it about 10-15 minutes to Washington Avenue.
Once you exit the train, take a left on Washington (heading south) for 1 block to 2727 Prytania St. It's called The Rink Shopping Plaza. This is the old Cresent City Skating Rink which now houses specialty shops.
Inside is a bookstore with 3 or 4 different books on Garden District walking tours. I bought the one entitled "The Historic Garden District: An Illustrated Guide and Walking Tour," and found it to be quite good. You could simply walk around the neighborhood, but having the book is very beneficial. It provides not only a history of the houses, but also some general neighborhood information. It's a great way to spend the afternoon.

Some of the mansions, though still occupied, are open for public tours, though there will be an admission charge. The Garden District starts a little beyond Jackson St. I highly recommend a walking tour.

You might start a walking tour by heading down First Street at its intersection with St. Charles. Proceed down to Chesnut and check out the lavender house on the corner. That's the abode of pulp horror goddess Anne Rice, and if you see a black limo outside, the Goth Queen is in residence. Then walk back up two blocks to Prytania Street (site of some of the neighborhood's most spectacular houses) and take a left, heading toward Washington, where you'll find Anne's bookstore and a cafe where you can stop and have a cup of tea. Then, take in Lafayette Cemetery on Washington, returning to the street to notice the Commander's Palace restaurant at 1403. Follow Washington all the way down to Magazine Street (now you're in the Lower Garden District) and indulge yourself in antique shopping and browsing second-hand stores.