So you need to rehome your pet?
First off, think of how many pets are out there already waiting for new homes, in shelters and rescues. And decide if you REALLY need to re-home, or if it's really just a convenience for you.
Behavior problems you may be experiencing with your pet can be addressed with the help of a professional trainer, or sometimes your veterinarian.
Sometimes behavior problems are actually health problems (hip displasia, for instance, or canine cognitive disorder, or even infections in elderly pets). If your dog has suddenly developed some bad habits, check with your vet first and rule out health problems.
Some dogs have unstable temperaments and have displayed aggression, in which case you should not rehome the pet, and, after a check up at your vet to rule out health issues, you may decide that euthanasia is the best and safest option for all concerned.
Please DO NOT give away or adopt out dogs with behavior problems hoping that some kind person will take them in. Bites are all to common and we need to try to prevent them.
If you're moving and think it's going to be too tough to bring along your pet, please go the extra mile, and keep calling around, ask friends for referrals to houses or apartments that allow you to have a pet.
Sometimes you have to pay a deposit to have your pet, but it's worth it to keep your pet as a member of your family.
If, after exhausting all avenues to keep your pet with you, you still believe you must rehome it, please have it altered prior to rehoming.
This will prevent your pet from adding to the problem of pet overpopulation and guarantee it's going to a pet home rather than becoming a potential puppy mill occupant.
http://www.petfinder.com has a classified area for people such as yourself. It is totally free to post there, but you must ask an adoption fee.
If you have altered your pets and given it all of its vaccinations, you should ask a fee to help cover those costs. $75.00-100 is not an unreasonable adoption fee for a fully vetted dog.
You should also check into having it microchipped, so you can keep track of it should it become lost or put in a shelter. Your vet can help you with this.
Asking a reasonable adoption fee ensures also that people will not "adopt" your dog on the spur of the moment decision, and helps ensure (but not guarantee) that your dog will be taken care of, healthwise and also socially. People who are willing to spend a bit of money on adopting a pet usually don't wind up tying it in a backyard somewhere where it will live the remainder of it's days. Dogs are social animals and need to interact with their families on a daily basis and you do not want your beloved family pet living on a chain and never seeing it's people except for feeding times.
Finally, if you've made the decision to rehome your pet, please use an application to get as much information on the new family as possible. Many people will not fill out an application, that's ok, don't feel bad. You want the best for your pet and this is how you will get the best home possible for it.
If the new home is in your area, either drive by or do an actual home check, perhaps when you drop the dog or cat off. Don't feel you have to let your pet go to the first home that applies - be choosy - you want the best home possible for your pet!
More than once someone has rehomed their dog only to learn the new family put it at the shelter, or let it go, or chained it to a tree somewhere or left it alongside the road and drove away. These are real, everyday issues, and you want to avoid them. Following the above suggestions will help!