Every time your pet changes to a new colour and/or species it will be added to it's Transformation Collection. There are many Pet Dailies that can change your pet's colour or species. Here are all of the Pet Colours your pet can transform into.
There are many different items on the site that will increase your pet's transformation collection. Using an Enchanted Plushie or Potion will change your pet to a specific species and colour.
A Costume will change your pet to a specific colour and a Fake Costume will only add the specific colour transformation to your pet's collection, without changing the pet's colour.
There are Enchanted Dips for every species of pet. You can use these on a matching species of pet and it will change your pet to a new, random colour. There is also an Essence for every species of pet and they will change your pet to a random colour of each species.