What qualifications must a "new" dog breed have before the AKC will recognize it as such?

For a start it has to be recognized by a legitimate kennel club.

The breed has to have been around for MANY DECADES

Follow the link that has already been provided for more details below is the first paragraph.

This paragraph you might find most interesting-

The FSS® is not open to "rare" breeds that are a variation of an AKC-registrable breed or the result of a combination of two AKC-recognized breeds. This includes and is not limited to differences such as size (over and under), coat type, coat colors, and coat colors and/or types that are disqualifications from Conformation Events by AKC breed standards

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How Breeds Enter the FSS®

The American Kennel Club considers requests to enter FSS® from breed clubs or individual fanciers of a breed. Those wishing to pursue recording with FSS® must:

Fill out a questionnaire for new breeds. Email: fss@akc.org for questionnaire.

Provide a written breed history documenting the distinct breed over a period of many decades. This should include details on any foreign and/or domestic organizations that register the breed. The source of the historical information must also be provided.

Provide an official written breed standard, indicating the origin of that standard. If the standard differs from the official breed standard in the breed country of origin please specify those differences.

Provide photographs of the breed, including puppies and adults, as well as both dogs and bitches. If there are different accepted types in the breed, photographs of each type should be included and labeled as such.

The AKC only considers adding new breeds to the FSS® or its registry upon request. The breed must be recognized by an acceptable foreign or domestic registry.

The FSS® is not open to "rare" breeds that are a variation of an AKC-registrable breed or the result of a combination of two AKC-recognized breeds. This includes and is not limited to differences such as size (over and under), coat type, coat colors, and coat colors and/or types that are disqualifications from Conformation Events by AKC breed standards

The parent breed club has to petition the AKC. They have to turn over their pedigree database, have a certain saturation nationwide in terms of registered owners, and most importantly, a breed club willing to jump through all the hoops to get them recognized.

Not sure what you mean. Do you mean a new breed you are trying to breed yourself or do you mean a breed from another country that AKC doesn't recognize at this time?

Have you checked the AKC website?

http://www.akc.org/reg/fss_details.cfm