Take the animal to your local vets and ask them to scan it for a microchip. If the animal is microchipped then they will be able to quickly reunite it with it's owner.
Check the 'lost' listings and create a 'found' listing at www.petsonthenet.co.nz. This is a national database and the key website we recommend everyone uses
Make a flyer with a clear picture, description and your contact details. Distribute it locally via notice boards, mailboxes, neighbours, community centres etc.
Knocking on the door and asking neighbours if they own the animal or if they know who does can speed up the process of reuniting the animal with it's owner
Embrace the power of social media to spread the word and try to find the owners. There are plenty of lost and found pages on Facebook that can be used
Look on the Trade Me Lost & Found section to see if anyone is looking for their lost pet. You can also advertise your found animal on here for free.