According to various Native American traditions- each person is connected with (several) animals that accompany him/her on his/her path through life. (Some of the things I've studied suggest you have nine that teach the directions and two that stay on either side of you- which are often seen in dreams, though I think it varies with individuals).These animals are said to be capable of nurtuing his/her talents and abilities. Since it is believed that all living beings are linked by a certain force, which in this case is seen as the Great Spirit, it is possible to invoke the animals directly.
In several traditions it is said that each animal teaches the wisdom of one of the seven directions: East-West-North-South-Above-Below-Inside
To describe the many unique and complex totem rituals that follow this would take too much time and space- as they are unique and differ between various tribes. However, it is possible to develop your own rituals- so long as the procedure makes sense to you and you use the typical characteristics of said animals. 
 Types of Totems:  
 Life-Long Animal Totem:  
Also known as the Spirit Totem. You may have one or multiple of these.Generally, they reflect you inner spiritual nature and are always there for you when you need them. 
 Journey Animal Totem  : 
This totem reflects a period of time. 
 Message Animal Totem  : 
Usually brings a message, self-growth, etc. 
 Shadow Animal Totem  : 
These are the totems that test us. 
 Various Animals:  
 **   Let it be noted that these animals and their characteristics vary between tribes and sources. I am simply compiling the most-used and most-known information about each. There are several others besides the one I list. Later I may cover mythological animal totems as well as insects and marine life  .  **  
Antelope :
The antelop tells us to "act sensibly". The antelop pursues a higher objective 
through its actions. The antelope will advise you to trust in your own strength 
and intuition. 
 Badger:  
The badger teaches us how to deal with power creatively. Most animals avoid contact with the badger, despite its small size. The badger is a dangerous adversary. People with this power can heal very well- as they are persistent. The badger teaches us to 
use our anger for changing unacceptable circumstances. Those with this power tend to be boss-like, and are capable of keeping everything going. They do not panic and are often thought of as having a "cool-head". 
 Bat:  The symbol of rebirth and a symbol of death. Bats live in the dark, however, when they sleep they tuck their heads down much like a baby before it's born. The bat tells us to face our fears. 
 Bear:  
The bear embodies self-observation. Many people follow the example 
of the bear and set aside time to be in solitude and reflect on themselves. 
The bear withdrawls into dreams in search for answers in the winter 
and is "reborn" in the spring. The bear teaches us the importance 
to recognize when we need to isolate ourselves from the world and 
take time to think. It is a symbol of strength and protection. 
 Beaver:  
Industry/Community- the beaver is the master builder. The 
power of the beaver helps us to realize ideas and work on them. 
It advises us to keep our options open. It tells us to believe 
in our dreams and strive towards making them reality. 
 Buffalo:  
The buffalo is symbolic of affluence. The white buffalo is a symbol of holy-ness. 
The buffalo teaches that everything exists in abundance if respected. 
It also points out that goals can only be reached through the Great Spirit. 
 Coyote:  
The coyote is both sacred and michevious. It is constantly tricking others. 
It does not usually learn from old mistakes, but it is good at 
making the best of any situation. People with the power of the coyote 
tend to act like clowns and find themselves in strange positions. The coyote 
is a mirror, drawing our own follies into light. 
 Crow:  
The crow is a guardian of secrets. It combines the past, present and 
future. It also combines light and shadow. The crow guards sacred laws. 
People with this power must stand firmly by their own realizations 
and strive to learn truths. 
 Dog:  
The dog is associated often with faith, loyalty and reliability. 
The dog is the guardian of its master and is willing to do many things 
for him/her. Throughout history it has been the guardian of things 
such as ancient knowledge. Those with the power of the dog 
are very compassionate. It teaches us to exmaine our loyalty 
towards others. 
 Eagle:  
The eagle is a personification of divine power. Often the eagles feathers have been used in various rituals. This animal brings the clarity of vision. It is capable of rising high into the sky, coming close to the Great Spirit, and is able to look down and observe things that might not be noted by others. It teaches the importance of recognizing the whole pattern of life. People with this animal regard both positive/negative aspects of life and learn how each serves a higher purpose in self- development. The power of the eagle is strength of the soul. 
 Falcon:  
The falcon is a messenger among the other animals. The message of the falcon is to accept the gifts you've been given. People who have the power of the falcon are often keen observers, who keep an eye towards the whole of things. They are able to recognize signs and receive advice. 
 Fox:  
It has the ability to "become one with the environment". It 
is often very observant, fast, and clever. The fox cares about 
family.People with the power of the fox are good at observation 
without being noticed. It teaches us how to use knowledge wisely. 
Fox-people are capable of "thinking outside the box". 
 Frog:  
The frog is linked to water. People who have the power of the frog 
tend to be good healers or mediums. This power allows them to cleanse 
their environment. The frog is a messenger of new life. 
 Hare:  
The hare represents fear. It is small, and thus is always in 
danger of getting killed and eaten. What you expect to happen usually 
happens, and the hare teaches that therefore what you fear will most likely 
happen as well. 
 Horse:  
The horse shows earthly strength. It is regarded highly throughout 
the world. With the help of the horse's speed- a person can cover 
long distances in a short amount of time. Riding a horse symbolizes 
freedom and teaches that power cannot be obtained through force, but 
instead through a respectful manner. Just as a horse carries a rider on 
its back, the rider must carry responsibility for the things around 
him/her. The power of the horse is to learn from the steps in one's life. 
 Hummingbird:  
The hummingbird represents life and happiness. It thrives in the 
beauty of nature. People with the power of the hummingbird tend 
to be able to "open others hearts". They are constantly searching for 
happiness, balance and enjoy helping others. 
 Lizard:  
The lizard symbolizes the dream-world. It teaches us how to use dreams 
to create a future. The lizard encourages us to examine our dreams 
and our shadows. 
 Lynx:  
The lynx is a bearer of secrets. If the power of the lynx is strong in a person 
they may have a special perception of the things around them. Through 
introspection s/he may learn many hidden things about the self. 
 Moose:  
The power of the moose is self-respect. It has impressive pride and strength. The moose teaches that one should express joy over achievements, just as the moose bellows challenges in its rutting season. The aim is not to ask for recognition, but to take enjoyment in personal success. It is said most elders possess the powers of the moose- they instruct younger individuals. Those with this power know when it is best to be friendly and when one should voice their anger. It shows how important it is to occassionally give yourself a "pat on the back". 
 Mouse:  
The mouse examines everything. It encourages us to look closely 
at the things we've established and form a system for the things 
we know. The mouse has an acute sense for danger. Mouse-people tend 
to be careful and extremely diligent, organizing various things. 
 Opossum:  
The "digression expert" of the animal kindgom. If all its defensive strategies fail, it will pretend to be dead and produce a scent of death. It has the ability to use its claws and teeth, but rarely does so. It teaches us to use our intellect to find ways out of tricky situations. 
 Otter:  
The otter symbolizes female energy. Its form is similar to Native American images of feminism- it is slender and graceful. It has a balancing power. It is motherly. It does not start fights though it will defend itself. It approaches everything with curiosity and friendliness. It is the power of sharing kindness and spreading joy. People with the energy of the otter tend to give free love. They do not tie themselves to material possessions. 
 Owl:  
The owl is a symbol of wisdom, magic and second sight. 
It is called the "eagle of the night". Owl-people can 
see through hidden strategies. They can grasp the whole truth 
of a situation. It is an essence of wisdom, as its acute senses 
allow it to hear and see things others would not. 
 Porcupine:  
The porcupine is symbollically similar to an "innocent child". 
It does not instigate turmoil, and if attacked it uses its spine as defensive mechanism. It is a 
friendly and loving animal. The porcupine teaches us to embrace faith and trust. Those with this animal tend to be open and discover new things to make each day exciting. It brings out the child-like sense in individuals. 
 
Raven:  
The raven is seen as a messenger and bearer of magic. It can help 
us change our outlooks and perspectives and learn great secrets. 
 Snake:  
The snake symbolizes the cycle of birth-life-death-rebirth. It 
sheds its skin and emerges new. It has the power of sexuality and 
the soul as well as transformation.Snake-People are hard to find, 
as these must be people who have experienced posion and transformed 
the posion into something else. 
 Squirrel:  
The squirrel is a gatherer- constantly building up stores of food 
so that it is prepared. It is very energetic, adaptable, and quick. 
People with the power of the squirrel find it hard to sit still. 
 Swan:  
The swans power is the gift of change. It evolves from a duckling 
to a majestic, graceful animal. People with the power of the swan are 
said to be able to see into the future. It teaches us balance of 
consciousness. 
 Tortoise:  
The tortoise embodies Mother Earth. Its shell is a hardened shield. 
It is slow, teaching us not to rush into anything. Its eggs hatch in 
the sunlight- telling us the importance of letting our ideas 
ripen before sharing. It teaches us to stand our ground firmly, and 
how to protect one's feelings and withdraw into ourselves. 
 Weasel:  
It was common for kings to wear garments and regalia made of ermine or weasel fur- because the weasel was known as an animal who can recognize "little details leading to great events". People who have the weasel as their totem animal are often underestimated, since their discretion does not allow for them to often reveal their insight, they have acute powers of observation. It is, however, a difficult totem as it is believed those who carry the powers of the weasel feel a "degree of responsibility" towards the things they notice about others: many become hermits and withdrawl themselves, as it is said that in the end knowing too much can make a person lonely and become a heavy weight on the mind. 
 Whale:  
The whale is a keeper of history. People with the power of the 
whale are usually very perceptive and interested in accesses old 
information. The whale teaches us to blend everything. 
 Wolf:  
The wolf, which is associated with the star Sirius, is a teacher 
and close-knit family member. It is capable of living with others 
without sacrificing its own independence. It chooses a partner to 
be faithful to its entire life. Its said that when the wolf howls 
at the moon it identifies with its spiritual energy. The wolf 
can give us the power to become teachers, to understand life better, 
and to make better connections between people. 
 Sources:  
 "Symbols of Native America" by Heike Owusu 
http://www.spiritualnetwork.net/totems/ 
http://www.crystalinks.com/totemanimals.html 
http://www.whats-your-sign.com