While AT&T's Next plan can be utilized to buy an iPhone via the online version of the Apple Store only, the company has already been testing the purchase of its iconic smartphone via Verizon Edge and T-Mobile JUMP!, at certain brick and mortar Apple Stores. For some reason, those two plans are not yet available to use with the online Apple Store.
The online Apple Store goes into detail, showing how AT&T Next would work with the purchase of a 16GB Apple iPhone 5s. The 12 month plan would require the AT&T customer to pay $0 down and make 20 monthly installment payments of $32.45. After 12 payments, the subscriber is eligible for an upgrade to a new phone. With the 18 month plan, the monthly installment price is $27.05 with an upgrade available after 18 months of payments.
source: AppleStore via 9to5Mac