Your chickens need to meet the American Poultry Association's Standard of Perfection. They have a book you can purchase that will explain all of the breeds recognized, the standards the judges look for, the disqualifications and defects for your breeds. This book has information on standard and bantam chickens, turkeys, and water fowl.
You'll want to show your chickens after they are fully feathered, to increase your chances of meeting the Standards of Perfection.
You will also want to get your show chickens from a breeder.
You can also look up breed clubs, they will often have the standard on their site. Many states require that the birds be tested for things like pullorum and AI. Here in MA, someone from the state comes down and tests the birds for free. You would attach a copy of the health certificate with your show entry.