There are several ways that witches and pagans use to find their totem animals.
A particular animal feels good to you.
Your own affinity with an animal.
Medicine cards
Read books on Native American culture and shamanism, and other books on animals and their symbolism in different cultures.
Perform your own ritual
Dreams
Meditative state
Vision quest
Simple Exercises to Find Your Totem Animal
Exercise 1
Research for the local animals in your area. Keep in mind that power animals are not limited to mammals. They can be reptiles, insects, birds, and fish. Make a list and study them carefully. Notice what they eat, their behavior, and their habitat. If you want, visit them in their natural habitat and watch them interact with the environment. Pay special attention to the legends and sayings about them. Remember, "clever as a fox, strong as an ox." You will find some pretty interesting things! Think of their strengths and weaknesses. Recognize these qualities working within you. In this way you will narrow down your choices.
Exercise 2
Take a sheet of paper and make a list of your good qualities. Be honest here! If you want, you can also ask your friends and family to write down all those good qualities they see in you. Sometimes we do not see many of our own good qualities, so this might help you see how others perceive you. Once you have a list of all your good qualities, start researching for those animals that have those qualities that represent your higher self.
Exercise 3
Perhaps this exercise will sound silly, but I found that it helped me more than I thought when I was looking for another totem animal. This is a very simple exercise. All you have to do is look around your room. Yes, you heard me right! Look around your room and notice those posters, figurines, and maybe stuffed animals you got over your bed. Have you noticed you have a tendency to favor certain kind of animal(s)? I know I did when I was starting! I looked around my room and all I saw were wolves and ravens in posters, figurines, stuffed animals, and more. Maybe you should consider it. It might be trying to tell you something. Reflect upon these questions:
"Why do you like that animal so much?"
"What characteristics does that animal have that you can identify yourself with?"
Another good way to find your totem animal is through a fast(although this does require the help of a teacher or elder). This was one of the first ways that I got in contact with not only my totem animal in the spirit world, but also over a three day period how I got in contact with some of my animal guides in this world or realm if you you will call it that.
Dreams as was pointed out in another post is a great way to find your totem animal. Meditation is also a good way, but I use herbs for smudging such as desert sage. Personal cerimonies are sometimes hard for newer people to do, and even in some cases only time will tell what your spirit animal is. Don't be to anxious to find things out...rememeber you'll find out the information when it's time for you to know. You're only given information or encounter problems at a pace that the creator and our spirit guides think we can handle.