Hundreds of years of selective breeding of just one wild chicken species, the red jungle fowl native to Southeast Asia, has resulted in dozens of vastly different breeds of chickens recognized worldwide. Developing a new breed takes an understanding to chicken genetics, current breeds and a lot of trial and error. Although there are many good books on chicken breeds, to develop a new breed takes a lot of knowledge you can only get from experience.
Decide what features you want in a new breed of chicken. Features to consider include color, standard or bantam size, feather type, top knot, and feathered or bare legs. You also want to decide if you want your chickens to be good egg layers or for meat.
Find out if the specific features you want occur with a dominant or recessive gene. If the trait is recessive, you will need two parent chickens with the trait to ensure the chicks have that trait. If the trait is dominant, then you may only need one parent with that trait. Other chicken breeders can help you determine this in some cases. However, if you are breeding for a new trait, then you will need to breed your chickens and document traits in chicks to determine if a trait is recessive or dominant and which chickens carry this trait.
Breed hens with roosters that each contain the traits you are looking for. Keep the breeding pairs in separate coops to make sure the right chickens are breeding.
Select the chicks that develop the traits you are seeking and breed those. It will take several generations of chickens and several years to develop a new chicken breed.