First of all do a LOT of reading about the breed. Learn the history, background, genetics (if you want), any genetic problems, etc. Learn what is a top quality cat in the breed - what to look for. Learn the standard inside and out.
And after you know your breed well, then start learning about breeding cats in general - what you need, problems, etc. You can find all this out in books - there are many good breeding/genetic books on the market. The breed ones might be a little harder to find, but check for these books on Amazon.com.
Attend cat shows in your area and watch the judging, talk to other breeders/owners of the one you like. Get to know the "lines" - what are good ones and ones to avoid. While learning history, you will learn these catteries with the better cats.
Most establish breeders do not like to sell breeding cats to a "novice". They have invested time, money, and want the best for their cats. Many novices think they want to show/breed and find out its more work then they thought and so get rid of the cats and the original breeder has no clue as to where their cats are or if they are being bred by someone else and where those kittens are.
So if you really want to breed, start at the shows and get to now the breeders/owners. THEN purchase a cat TO BE ALTERED and show that cat. You will have a chance to really get to know the breed and find out if showing/breeding IS what you want. If you are successful in showing that cat and have established a reputation as a good owner, then you can seek out your breeding cats. Start with a breeding female - not the males as they will most likely be caged and harder to handle at times. You also want to get a "mentor" to help you with breeding and how to tell pet quality from show quality.
You have to know something about genetics and lines so you know what cats to put together. You don't just breed your cat to any old male of that breed - you want the best male and female being bred to produce quality cats and IMPROVE the lines - not just to breed mediocre cats for money.
This process can take as long as 5-10 yrs. I showed cats (alters) for 5-8 yrs before I got my breeding female. I knew the breed inside and out. It was another 5 yrs before I got a breeding male. I would prefer to keep a breeding female and send her out to a stud then to keep the stud as its a lot more to take care of a stud. Whole males will spray and you can't let them be running around the house with whole females. You need to plan your breedings. Females shouldn't have any more then one litter a year unless its a litter of only 1 or 2 kittens - but you still should have about 9-10 months of time between pregnancy/delivery, recovery.
And if you want to be a good breeder, you will have a contract for the owners to spay/neuter the kittens by a certain time. YOU should be responsible for EVERY kitten born of your females - that is a responsible breeder!