You can get an inexpensive small dog of your choice from accredited dog breeders, backyard dog breeders, pet stores and dog adoption agencies or dog shelters. You can contact these various dog owners and get the dog of your choice.
Figure out what specifics you're looking for in a dog and go from there. I found that petfinder.com was a great way to find the dog I wanted at a shelter. I've also purchased 2 dogs at our local pet store and paid quite a bit so I'm sticking with shelters from now on.
If you don't want to pay a lot of money, PLEASE do not get a dog. Dogs cost LOTS of money. If you find one for free, their food, vet bills, supplies, etc are really expensive. If you can't afford one initial cost, you can't afford the money it takes to keep one. Dogs cost almost $1,000 per year (if they are healthy and have no major medical issues) and little dogs can live around 20 years!