Question: How do I get into dog breeding?
Answer: The answer is not a simple one. There are several factors to consider. I am going to assume you have done breed research and know what breed is best suited for your lifestyle.

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Selection of a Breeding Dog
First you need to start with a good quality dog, worthy of being bred. The dog must be a registered purebred of good quality. Dogs purchased in pet stores are not considered breeding quality. Pet stores sell "pet quality"animals. If you are interested you must start by researching a breeder who takes their dogs to shows prior to breeding them, thus proving their dogs are excellent quality, worthy of producing puppies. The breeder will have ensured both parents were checked for breeding soundnesses as related to the breed. Typically hips, eyes, and ears.
If you are unsure of how to find a good breeder, pick up a dog magazine and look through the ads, the breeder should be in good standings with their dog club. You can also ask a veterinarian, animal shelter, or groomer if they know of any good breeders for a certain breed of dog. You can attend a dog show and meet dog owners and breeders there. Seeing their dogs first hand is also a big advantage. You have to separate the good breeders from the "backyard-breeders", the main way you do this is by checking show records on the dogs.
Make sure the breeder can demonstrate that both parents have earned championship titles to show the worth of their animals. This will mean your pup has a much better chance and being a quality animal worthy of being bred as well. You should be able to meet the mom of the litter, make sure she is friendly and approachable. Temperament is partially genetic, and partially learned from their mom. You may or may not be able to meet the sire (father), as some breeders only own the female dog and use someone else's male dog.
Most good breeders have waiting lists for pups. If you are serious about becoming a dog breeder you must be willing to wait. Ideally you want first or second pick of the litter. Do not take the runt. If the breed has certain standards for color, be sure you check the pup for color and markings. Look for one that is bright and alert. Have the breeder mark which puppy is going to be reserved for you, and get a written contract.
Breeders cannot advertise purebred pups and offer them at one price with papers, and another price without. If your breeder tries this, I suggest you look for a different breeder, or point out to them that this is illegal. It is unlikely a reputable breeder will try this. They can be reported to their kennel club if this comes up.
Reputable breeders always offer health guarantees on the pups. They always have the pups vet checked, vaccinated, and dewormed before selling them. Good breeders will not let their pups go before 6 weeks of age, and many wont let them go until 8-10 weeks of age, especially for smaller breed pups. Do not accept a puppy under 6 weeks of age. Never pay a cent for an non-vaccinated pup who has not had a vet check. You could be in for a nightmare of expense.
GettingYour Dog Ready
You must properly socialize and train your pup. Take it to formal lessons. Work with it when you are home to make sure it is developing mentally. Formal lessons have the advantage of teaching dogs how to socialize with other dogs and how to pay attention to you in the midst of distractions.
As the dog matures, you will need to take it to shows to prove its worth as a breeding animal. It should not be bred until it is two-years-old and has proven itself to be an excellent example of the breed worthy of passing on its genetics. As you attend shows you will meet contacts, both of whom may be interested in future pups from your dog, or be interested in breeding their dog to yours. If after 2 years your dog has not been able to earn any titles, then you might have to resign yourself to the fact that the dog is not of breeding quality, and should spay or neuter the dog.
Finally you must take the dog to the vet to get the proper checks done prior to breeding. Depending what country you are in these checks are referred to by different names, but they basically check things like hips, ears, and eyes.
Selecting a Mate
Select a mate who has also attained show credentials and proven themselves to be an excellent example of the breed. Try to select a dog who makes the best of any weaknesses your dog has. You will have learned this from showing. Agree on a stud fee, sometimes this is "pick of the litter", but what if there is only 1 puppy? Make sure you have a written breeding contract, and both of you should have signed copies.
Next
Beyond this is up to you. Depending if you own a male or female dog. How to care for a pregnant dog and how to raise pups are a whole other issue. You can research that as well. If you own a female dog, you do need to be prepared for disaster, especially if its a small breed. Make sure you have sufficient funds in the bank to cover any emergencies, such as Caesarean sections.
Moral Issues
Millions of dogs and pups are euthanized every year in USA alone simply because people do not put any thought into breeding their dogs. By making the decision to become a breeder you are potentially contributing to a problem. The bulk of the problem lies with people who breed simply "because they can". People who do not make sure their dogs are of breeding quality and breed because their dog is "cute". As a reputable breeder you will not get rich. Breeding dogs is solely for the purpose of improving the breed, not for improving the kind of car you drive. Reputable breeders breed because they care about the breed and are passionate to improve it.
Finally breeding is a risky business, at any moment you could have a problem. A reputable breeder is always willing to take back any problem or unwanted pups. They do not breed until they have a waiting list ready for people who want pups.
Spayed and neutered dogs make better pets and have fewer health risks. They live on average 2 years longer. If you are looking for a companion to love and care for, do not get involved with breeding. Unless you have a lot of time to devote to showing your dog, and a lot of time to screen potential owners for pups, do not get involved in breeding. Keep your dog as a pet and love it solely for who it is.