I guess through meditation. I am under the belief that you ask to have your spirit animal come to you. I have tried, but am unable to go that deep in my meditation. Although, after the meditation, I have had pretty strong animal response the following day,which was very fun and amusing, and , haven't followed through with finding what my animal guide is. Don't forget that certain animal guides will come into your life to teach us a lesson or give us a message, then be gone and off. Good luck in finding your guide. I often think about trying again. Let us know how you do.
And maybe try pinpointing more of an animal that you relate to or are fascinated with.