Reservations can be made on their website at: http://chick-fil-aforbreakfast.com.
On the site, you may choose your preferred location, the date, time, and breakfast entree. A few locations are low but most still have an ample supply of reservations available at the time of this writing.
Breakfast items offered include: the Chicken Biscuit; Spicy Chicken Biscuit; Sausage Biscuit; 3-Count Chick-n-Minis; Chicken, Egg & Cheese Bagel; Bacon, Egg & Cheese Biscuit; Chicken Breakfast Burrito; Sausage Breakfast Burrito; Oatmeal; and Yogurt Parfait.
Reservations can be made through 12am on September 13, limited by availability.
If you're wondering why Chick-fil-A requires a reservation, it helps them manage the crowds so that customers aren't kept waiting and customer service doesn't suffer. They've offered several similar reservation-based food freebies in the past.