It is usually considered improper to try and reach upon a spirit animal, and trying to contact it and "ask" or find out if it is your animal. It is almost like asking a married woman, to go out on a romantic date with you.
Usually, what happens is that the spirit animal will contact you, but you must do your fair share and allow spirits acknowledge your willingness and openness. A method could be by saying a simply prayer, asking for a spirit animal, but you do not chose which. Then, after such, keep your energies open and flowing.
Another method is to open and balance your chakras, and allow proper energy to flow throughout your body. Then, you should meditate on common animals, such as dogs, cats, birds, wolves, etc. You may even try insects. You may feel a certain "drawing towards" to one. Of course, you may if it is your favored animal, but I suggest you leave your favored animal away from mind unless all else does fail.
I have heard of astral projection allowing you to meet your spirit guide, but I do not really support this, as you may meet an array of spirits who can easily claim to be your guide.
Star is incorrect. It's okay to find out your spirit animal at any time in your life! There are many ways to go about it but the best way, in my opinion is to meditate on it. I actually visualized the whole thing. Not like astral projection or pathwalking or anything like that. Just a visualized meditation.
I was walking a dirt path in an autumn forest at sunset. I cleared my mind and shifted my awareness to my objective. But for some reason, I couldn't block out this fox that seemed to be following me. It followed me all the way to this cliff. I looked at it and asked,"Are you my spirit animal?" to which it replied,"Yes." and dove back into the forest.
For me I just meditated. I imagined myself walking across a bridge dumping my problems into a river below and accepting beyond the shadow of a doubt that my spirit animal would be waiting somewhere in the forest beyond the bridge. I walked for a while until I found a deer, which is what I was expecting to find. However when I reached out to touch him, he transformed into a beautiful black and white clydesdale.
I've always had a deep connection to horses and having one as a guide just makes sense. I saw a deer only because I was expecting a deer.
I have had other guides over the years, for a times there was a hare and a hawk, both stayed by me for a few months to teach me lessons. The hare wanted me to learn to remove myself from difficult situations rather than staying and fighting. Hawk sought to teach me to see problems from a new perspective. There was an octopus too, he came to me in a dream and told me all about how I was letting too many other people steer and control my life. None of these other guides have been permanent figures but I learned from them all the same.
I've also heard that its particularly helpful doing meditation somehwere with a lot of nature not near moderns civilization some place like yellowstone or a nature preserve.