Ensure that the animal is up to date on all of their vaccinations, and are spayed and neutered. Make sure that their veterinarian records are ready to be passed onto the new owner.
Advertising Your Pet
Never use the word 'free' in your advertising. Even if you plan on giving it away without cost, you'll attract a lot of attention from the wrong kind of people. Remember, anyone adopting a pet should be stable enough to provide proper diet, exercise and health requirements that the animal comes with.
Don't be afraid to ask for help from local shelters, and care societies. If you have to find your animal a new home fast and are having trouble, you can take the pet to these places as a last resort. If you contact them ahead of time, they may be able to include your pet in their advertising for pets available for adoption.
When it comes to finding the right home for your animal, trust your gut instincts. If you're not 100% convinced that you've found the perfect fit for both the new owner and the animal, your subconscious is likely picking up subtle hints to cause any uneasy feelings.