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.