AKC requires you to keep a Dog Ownership Record for each dog you own. You can click on the link below, download the form and print it off. The only other thing that is required is that all Litter Records must be up to date. If AKC does a home visit these are the only two forms of record keeping they will want to see.
http://www.akc.org/pdfs/DogRecord.pdf
AKC also has some online record keeping available but that is optional.