You can find out what your spirit animal is right now with a quick guided meditation. This is what I used to discover that my spirit animal is the Otter.
If the guided video meditation doesn't work for you, another option is to notice signs. I discovered that the Penguin was my spirit animal because I kept on seeing signs of the penguin throughout the entire day. I took the train and saw someone with a penguin backpack. I got home and turned on the t.v. to see a commercial about penguins. Things like this are not coincidences. If you notice them, you will know its a sign from the other realms. During this time, I was first learning about astral projection and lucid dreaming, but I was struggling with it. So it was no surprise when I looked up the meaning of the penguin and it said that Penguin helps us with out of body experiences! I started keeping a dream journal and I asked for Penguin's help in achieving astral projection. After I asked, I literally felt that I was embodying the penguin. I researched and learned more about penguins. The first time I achieved astral projection, I imagined I was a penguin...the master of both water and land. I pictured myself emerging from the icy cold waters into the land and I was out of my body :)
So all you have to do is ask for your spirit animal to show itself to you through divine signs.