With one exception (the AKC Invitational), the AKC does not put on dog shows. The American Kennel Club is a club of clubs. The AKC provides the rules for shows, licenses them, certifies judges qualified to judge at shows, and provides a mechanism for discipline in cases of violations of rules. The shows themselves are put on by the clubs, whether member clubs or clubs licensed by the AKC to hold shows.
Clubs may be one of three kinds. All-breed clubs are open to fanciers from all AKC-recogized breeds. These clubs serve a local community. They may be old and prestigious, like the Westminster Kennel Club, large, like the Houston Kennel Club, or small and relatively new, like mine, the Warren County Kennel Club of Ohio. Best named club: The First Company Governor's Foot Guard Athletic Association, located in Hartford, Connecticut.
Specialty clubs are devoted to one breed. The latter kind of club may be local, like the German Shorthaired Pointer Club of Greater Pittsburgh, or national, like the Clumber Spaniel Club of America. National breed clubs are the recognized parent clubs for their breeds. Only these clubs have the right to fix and alter the standards for their breeds. If a breed has several varieties, the national club includes them all. Thus the national specialty show for the Dachshund Club of America would have all three Dachshund varieties - Smooth, Wirehaired, and Longhaired - even though these are shown separately at all-breed shows.
There may also be limited breed clubs devoted to one of the seven variety groups. For example, the Montgomery Kennel Club show is for Terriers only and the Western Hound Association of Southern California devotes itself to Hounds.
AKC clubs are incorporated, non-profit organizations (the few for-profit clubs, like the Detroit Kennel Club, are grandfathered in). Their organization is similar, with a president, one or two vice presidents, recording and corresponding secretaries, treasurer, and board of directors. The board of the Westminster Kennel Club is all-male while the board of the Ladies Kennel Club of Boston is all-female. Instead of a board of directors, national clubs will have regional governors representing the various parts of the country. My lovely bride is a regional governor for the Borzoi Club of America. In her travels on the show circuit, she occasionally holds meetings with the membership in the upper Midwest, reporting on the doings of the club and taking back to the board the concerns and suggestions of the members.
What does it take to be an AKC-recognized club? The information on how to do so is here. In short, it must serve a local community of fanciers; it is more difficult to have a recognized club if there is another in the area performing the same function. The AKC determines this on a case-by-case basis and there are no fixed radii within which a club cannot be formed.
It needs an organization and records indicating it is serving the interests of the community (holding meetings, putting on fun matches, etc.) and to correspond with the AKC. It also needs a show site suitable to hold shows. After a year in business, the nascent organization can apply to the AKC. For this it needs a record of activities, a list of members, how active in the fancy they are, an operating board, and a constitution and by-laws.
A club then needs to prove that it can put on a show. It can apply to the AKC to hold matches (a kind of practice show at which championship points are not given). Successfully holding these events allows a club to apply for licensed status. It again must detail members, organization, and activities. If approved, the club can start giving AKC-licensed shows at which championship points are awarded.
After 10 years of continuous operation, a club may apply to the AKC for member status. Service to the community, membership growth, and a history of successful shows can permit a club to become a member. On attaining membership status, a club can name a delegate to the AKC's Delegate Body. This delegate body meets quarterly and is the sole power that makes rules governing dog shows. From it, the AKC's Board of Directors are chosen. At present, there are some 500 member clubs and about 4000 licensed clubs of all kinds (conformation, obedience, and field).