Your power animal is what you make it. There's no special requirement, ritual, or shamanic journey that you need to take to claim a power animal. Accepting it in your heart is perfectly fine. If you want to honor your power animal though, there are tons of ways that you can create rituals, spells, or meditations to spend time with your new friend.
In any case, the most popular power animals that we've seen are, in no particular order: