After you click on the $ Buy Now button (and log in, if you haven't already), then click on the blue YES button just underneath the REDEEM ANY GIFT CARDS OR PROMO CODES section. Use coupon code 1stbirthday, click on Apply and verify your total before completing the purchase. If you've picked an agency priced book or already used the code, you'll see an error message and the order total won't be adjusted.
Also, I see that they have finally added the ability to not only set up gift cards (or send them to other people), but have also added the ability to send a book as a gift. I haven't tried it out yet, so I don't know if the coupons work on those (let me know, if you do).