I don't like the term "totem animals".
There are two types of spirit animals worked with--your spirit animal guide/guardian and your spirit animal medicine (sometime referred to as "power" or "totem" animals). Your spirit animal guide/guardian is not chosen, but chooses you like any spirit guide. It is an animal that comes closest to your personality/spirit in personality.
In spirit animal medicine, you choose the animal you wish to learn from. By picking an animal with personality traits or skills you desire, working with them and connecting with them, they can show you their ways and help you to succeed in the goal you have set.
I wrote about how I do this here
When you work with spirit animals, its good to have some form of representation of them carried with you.