Start with all the free pets from the
adopt page! These are updated every month.
You can also get pets from the
pound. It opens at random times, so keep an eye on that page. If you're lucky, you can get old and valuable pets!
Finally, there's the
free adoptions forum, where users give away their own pets for free. I recommend looking for quitting users, as they'll often let you take a lot of pets and they're more likely to give out valuable pets.