You could advertise locally-be sure to get references & check why they want your dog. You want a solid, loving & caring environment. Vets often have lists of people that want dogs & the vet checks out the request ( more throughly, if you request it). Going to websites may help you-but I would handle this myself if possible.
Are you giving it away or selling it? If your just giving it away you can take it to a pet rescue (not a pound) and will keep it until they can find it a great home! They do not euthanize them! Hope this helps!!
If you find new owners yourself, check them out first, i.e., do a home visit to be sure it won't be chained outside, find out who their vet is and ask about them, watch their interaction with the dog, etc...
You can't be too careful. There are a lot of good people out there - but there are also a lot of bad ones.