This article is a more in-depth look at what I feel is important when choosing a breeder. Obviously, these are just my opinions, they are opinions based on research and experience, but opinions nonetheless.
This is just a quick look at selecting a breed, there are many resources available to help you with this, this is intended merely as a brief overview. There are some things you can change about a dog, you can cut its hair and make a longhaired dog into a shorthaired dog, for example, but there are two things you cannot change: you cannot change a dog's exercise needs, and you cannot change what the dog was bred to do. A breed is the product of generations of selective breeding to produce a true-breeding animal which has a certain set of characteristics, some are related to appearance, others are related to behaviours which occur naturally in canids, but honed and distilled (herding, for example, is rooted in stalking/hunting behaviour). Expecting a dog to behave in ways which are opposite to what it has been bred to do is unreasonable. You can redirect drives, but you cannot erase them. Part of successful dog ownership is educating yourself about what your dog's breed is intended to do, and finding ways to direct your dog's bred-in drives into behaviours which you find acceptable, but which still allow the dog an outlet for those drives. Chewing, for example, is a normal dog behaviour (especially in puppies), it's unreasonable (and therefore doomed to failure) to expect a dog NOT to chew, but you can most definitely teach a dog what he can and cannot chew. Another part of successful dog ownership is making wise, self-aware decisions about how much exercise you are prepared to give your dog. Many dogs end up in shelters and rescues precisely because their orginal owners did not have reasonable expectations about how much exercise the dog needed. A Lab, for example, is a dog bred to work hard all day in terrible weather, running through fields, retrieving birds from cold lakes, spending all day outside working with their owners. They are not dogs bred to lie on the couch eating bon-bons, and their sweet, trainable nature means they often end up in homes which do not provide them with the level of exercise they need to be happy, healthy and well-behaved. A tired dog is a good dog. In short, make appropriate decisions about how much exercise you can give a dog, and make reasonable estimations of what behaviours you cannot accept (if you are someone who takes a lot of pride in a tidy garden, a terrier, with its love of digging, might not be a good choice, for example). Attending some dog shows is a great way to see and meet a number of different breeds and get a good idea of which ones might suit you (contacting your country's kennel club will help you find shows in your area).
So, let's assume that you've narrowed down your choices, you've attended some dog shows, you've done your research into different breeds, you've found a couple which might meet your requirements in terms of instincts and exercise needs, and you're ready to take the next step. One of the best places to continue from here is to find the breeds' national breed clubs (normally called "The (breed) Club of (country)", or something like that, Google is your friend here). My next step at this point would be to contact a few breeders (maybe some you've met at dog shows) and make arrangements to meet their dogs. When I was researching Swedish Vallhunds, I traveled to meet three different breeders and their dogs, and by the time I brought Rakki home I had met over a dozen different Vallhunds (and Vallhunds are an uncommon breed).
A breeder should want to know quite a lot about you before being willing to place a puppy in your home. They want you and your puppy to be happy with each other, and they will need to ensure that you are willing and able to provide the sort of home that their breed requires to do well. Many breeders ask you to complete a questionnaire, including specific questions about your home, your yard, your intentions regarding exercise, feeding, vet care and training the dog, and many will ask about your past pets (including their ages at, and causes of, death), and ask for a referral from your veterinarian.
The letters you see before and after a dog's name can tell you important things about the dog.
A "conformation title" (usually a championship, often abbreviated as "CH") means that the dog has won a required number of points, including being placed ahead of a required number of dogs, by a certain number of judges, at a certain number of shows. People like to call conformation shows "beauty contests" in a disparaging way, but they are more than that (and such comments indicate a degree of ignorance about conformation showing), they aren't about which dog is prettiest, they're about which dog most closely resembles the ideal breed type. The original intent of conformation shows was to evaluate breeding stock. The dogs are compared individually to their "breed standard" (a formal outline of what the breed is supposed to look like, and what characteristics it is supposed to have), and the dogs are placed in order of how closely they meet the standard. Because the judge is a human being, there are personal preferences, opinions and sometimes politics involved in class placements, but overall a conformation championship is one piece of evidence that someone other than the dog's owner thinks that a dog might be suitable for breeding. It is very far from everything that is required to ethically breed a dog, but it is one important piece of data.
A "performance title" (usually after the dog's name, but sometimes before, depending on the title) means that the dog has completed specific exercises in a specific fashion, to earn a required number of points to earn a given title. Most performance titles have levels, for example the most basic obedience title in AKC and CKC is the Companion Dog (indicated by a "CD" after the dog's name, except for the UKC CD, which is normally indicated by a "U-CD" before the dog's name), dogs who have earned a CD can then go on to complete the requirements for the next level obedience title, the Companion Dog Excellent (CDX), followed by the Utility Dog (UD), Utility Dog Excellent (UDX) and finally the Obedience Trial Champion (OTCH). The various kennel clubs have detailed outlines of the requirements for the various titles they offer, and you can observe obedience and other performance classes at many dog shows. Performance titles are offered by most kennel clubs, in obedience (a formal form of basic dog training, including heeling patterns, sit and down stays, retrieves and at higher levels, scent discrimination), rally (a more informal, fun form of obedience, but very challenging at the higher levels, including such exercises as heeling backwards and sideways), agility (dogs run a course of obstacles in a specific order, including jumps, teeter-totters and weave poles), herding, hunting and other areas. A performance title is a piece of evidence that the dog is willing to work with a handler, possesses the instincts it should have (depending on breed) and is capable of being trained to the level required to earn a title.
Dog breeding is a crap shoot, the best an ethical breeder can do is do their best to stack the odds in their favour. There are so many variables involved with genetics, that there are very few hard and fast rules about what you'll get if you cross a given dog with a given bitch. However, since there are so many variables, the ones over which we have any control whatsoever should be used to our advantage. We know certain conditions are genetic, we know other conditions might be genetic, and we have tests available to us which can test for some of these conditions. Part of responsible dog breeding is learning what you can about your breeding stock's genetics, and making educated, careful decisions about the matings you undertake. "Doubling up" genes which code for health problems (by breeding dogs who are carriers of those genes to each other) vastly increases the likelihood that the resulting offspring will have those health problems. This is why researching both the depth (ancestors) and breadth (siblings and partial siblings) of pedigrees is important for breeders.
Conditions like hip dysplasia are "polygenetic", which means that the problem is coded for on more than one gene, this condition in particular requires attention to pedigree breadth: a dog whose hips are rated "OFA Fair" for example (see the OFA's website for details), but whose siblings and partial siblings all have "Good" or "Excellent" hips, is often a much better prospect genetically (at least in terms of hip dysplasia) than a dog who has "Excellent" hips, but whose relatives have symptomatic hip dysplasia. The fact that the problem hasn't actually affected the dog doesn't mean that the dog doesn't carry the genes for it, and looking at the whole genetic picture means that you can make a more educated guess about what the dog's genes actually code for. Which is not to say that you shouldn't breed the dog in the second example, but you might mitigate some of the risk by breeding it to a dog whose family's hips are predominantly "Good" or "Excellent".
Health tests won't guarantee that the puppies will be healthy, but they certainly help to reduce at least some of the risk.