Even though most rescue organizations are breed specific, there are also some that specialize in different types of dogs—large, small, pit-bull types of herding types, or they cater to geographical regions. A lot of these rescue groups look in shelters for dogs who need to be adopted before their time is up, and they accept owner turn-ins.
Talk to your vet, local animal shelter, or a breed club when looking for a rescue. Most of the rescue groups screen their dogs thoroughly, and they only place those who are healthy and socialized. You should have lots of questions for the rescue staff, and they will probably have lots of questions for you. Lots of these rescue groups work hard to match the right family with the right dog. They will ask you how often you are at home, what your activity level is, who else lives in your house, including other pets, how secure your fence is, and what type of activities are you planning to do with your new dog. Depending on the philosophy of the breeder, they might encourage you to give the dog a certain type of food, do a particular activity, or even have one person at home all the time with the dog.
Dogs in these rescue groups have been abandoned once before, so volunteers have a commitment to keeping them from the same thing happening again. To be interviewed, most of them will ask you to fill out an extensive application. To avoid the problems that landed the dogs in rescue facility in the first place, they really do their best to pair up dogs with the right families. When you adopt from a breed rescue, you have a great way to find the exact dog you desire, while still saving a life.