Mine came to me in a dream. Some spiritual dreams, or "numinous" dreams if you want to get fancy about it...well, they have a different texture than most other dreams. In that, I felt a connection with a Wolf...and kind of woke up disappointed. Like, "Wolf? Seriously, wolf?" I have never seen a real-live wolf. Wolves are not native fauna in the country I was born, raised, and now live in. But I felt such a sharp resonance that was bonding us...
Since that was my first brush with anything really animal-shaped in my practice, I thought that it was my own spirit animal, which it was but not in the Norse fylgja sense (which is closer to what most people mean, I think, when they say something like "totem"--originally a totem was for a whole family, not only one person). Instead, it was a symbol...spirit guide sort of...to work with me through a particular issue, which was the meaning of a "pack" or family and my relation to my family.
If there really is a non-human animal shaped part of my soul, I can't even imagine what that sharp resonant bond is going to feel like! But I personally am back to the opinion to that not everybody has one...or, if it reveals itself, it'll be in its own time.
"Fur and Fang, Blood and Bone" by Lupa (Rebecca Luxa) is interesting to read on this topic, though.