So you no longer can take care of your dog. Here's how you can find a nice home that will care for and love it.

[edit] Steps

Make sure you really want to do this. It is a big decision. If you are giving up your dog for behavioral reasons, try a trainer first.
Ask people you know if they want the dog, and to put the word out to their own networks.
Put up signs that say there's a dog for sale with your phone number, to where someone who wants the dog can buy it.
Posting an ad to Craigslist is a very good way to find a home for a well behaved dog.
Screen anyone who is interested in your dog. You can search for applications used by rescue groups around the country. Modify it for your needs.
If your dog is a purebred of a recognized breed, contact a local breed rescue organization. they are easily found by using Google or another Web search engine.

[edit] Tips

Taking your dog to the Humane Society or anywhere where it could get euthanized should be your last resort.
It is better to take your dog to the Humane Society or the pound than to maltreat your dog, or simply setting it free to roam the streets.
Get the dog spayed / neutered and fully vaccinated. That way you can be sure that an unethical breeder will not get your dog, and rescue groups are more likely to take it.