Meditating, as suggested, is a good way to find out what it is. When meditating, focus on the intent to discover which one(s) are yours.
Make a list of your traits or qualities, then have someone you know check to make sure you listed them correctly. Think of animals that may correspond to this.
Keep a dream journal!
Sometimes you may have dreams about animals like the one you experienced. These can be very good indicators. Try to determine what it was like in the dream and keep track of details. What happened? What did it look like? So on.
Generally, you'll feel a close association with whichever animals are yours. So follow your instinct. Of you have one in mind, like the hawk, research that animal a bit.
My Spirit Animal is a Wolf I found it through meditating for 6 years and found it. Somtimes you discover it later in life and or it comes to you in a dream or in reality. Iv heard that if one discovers his/hers S.A. they will obtain powerful spiritual properties.
Messages from spirit
Recalling past lives
Seeing the larger picture
Wise use of opportunities