Hello, Eros!
Great question!
I prefer to book my Advanced Dining Reservations through Disney's online Dining Reservation system, as it allows me the greatest amount of flexibility. I can book in the middle of the night, see multiple reservation options all in one glance and can more easily track my reservations using the new My Disney Experience option on the website as well.
What's more, if you have a smart phone, you can download the free App "My Disney Experience" which will enable you to see those online reservations right on your phone. In addition, you can add Guests to your reservation, then select "share" with those other Guests, enabling them to see these reservations on their "My Disney Experience" App as well. I can't wait to utilize that feature on our upcoming trip to WDW, so my husband and teenage daughter will be able to check their own calendars in the App to know when our reservations are each day.
You can always inform a Cast Member at the restaurant check-in that you're celebrating a special day, too. For more information about ordering Specialty Cakes or other celebration options, take a look at this page entitled
Customize Your Special Occasion.
Of course, should you prefer to speak with a Cast Member and have him or her add your birthday celebration to a new or existing reservation, you can simply call (407) WDW-DINE; they are always so happy to help!
Send more questions as you think of them, Eros; I love to help, too!