One thing I've always had trouble with when building a world is developing cultural myths and beliefs that feel unique and special from Earthly culture. Specifically, animals' meanings. In Christianity, for example, a snake is a symbol of evil. In America, the eagle is a sign of freedom, Etc. I need my myths to feel realistic.
What process can we use to create animals meanings?
What leads cultures to choose specific animals for specific meanings?
The most important point is: Notability. It must be an animal that is, or was at the time the myth was formed, something people would notice. That is, it has to be fairly common, and also in some way special. It may be that it is useful (like animals you eat). It maybe it is dangerous. It may be that it is a sign for important dates or events (think of migrating birds returning in spring, indicating the end of the winter). It may be that it is a rather impressive sight (like the eagle). It may be that it has some extraordinary abilities. It may be that it has some extraordinary feature which asks for explanation. Or for people coming to a new place (for example, the elements), it may be an animal that is different to the animals known from the old place.
Here several sources are possible:
Typical (real or perceived) traits of the animal. For example, the pig likes to wallow in mud (it's both a way to regulate body temperature as pigs can't sweat, and a way to deal with parasites). That's why pigs are perceived as dirty animals. In addition, the meat of pigs can easily cause illnesses if not treated right, which adds to the perception of dirtiness (dirt makes you ill, so pig meat makes you ill because of the dirt).
The relation of the animal to the human. Farm animals are likely to signify luck or wealth. Animals that are a thread to humans, to farm animals or to food supply are likely to be associated with evil traits.
Special features, and the way those get explained. For example, the Dalmatian pelican gets a red spot on the throat during breeding season, which gave rise to the myth that pelicans feed their young with their own blood if no other food is available, which affected the symbolism of the pelican as especially caring for the young, and as symbol for the passion of Christ.
Association with other symbols (animal or otherwise) for the same thing. For example rabbits are commonly associated with fertility, for obvious reasons. Similarly eggs are associated with fertility. The association of both with fertility (and thus with spring and then specifically Easter), led to associating them with each other, and ultimately to the myth of the rabbit bringing the Easter eggs.
Distinction of the own culture/religion from other religions/mythologies. For example, the cat (a very useful animal that catches rats and mice, and therefore protects from food loss and illnesses) was seen as very positive by the ancient religions, and that was the reason why Christianity associated them with the devil. Indeed, I've once heard somewhere that the fight against cats was one of the reasons why the pest could get out of control. Also the fact that the snake in the bible is evil might be a reaction of the snake being considered a positive animal by the surrounding religions.
The most important prerequisite is that the animal in question has to be native to the region the people live in. You wouldn't expect, for example, people living around the equator to have myths involving polar bears.
Next, it usually has a profound impact on the society. Animals can serve as food, so they might be the avatars of the god of fertility, or even the creator of all living beings. Animals can be predators, maybe even pose a threat to humans, so they might be representative of a vengeful god, a god of war, a destroyer of worlds. They might just be an accidental threat, like scorpions, representing Death and the underworld.
The physical abilities of the animal also influence the properties attributed to it, by process of anthropomorphization.
How an animal is viewed can also depend on the type of society. While a pig could represent fertility and benevolence of the gods to people in a hunter/gatherer society, it might be a symbol of fortune and wealth in an agricultural society, and a low, dirty animal (tended to by low, dirty humans) in an urban society.
As for practical advice: Don't be ashamed, read up on animal myths as they exist(ed) on Earth, and draw inspiration from there. Better use a good copy than a bad original.
Many totemic animals are selected because they have qualities which we wish to emulate, or to signify some of our powers to potential mates or foes. This is why the garden slug is not often evoked as a totemic creature or the symbol of a cult figure or a god. Now if garden slugs were the size of semi trailers, there might be a change in attitude....
Since as far as we can tell, early cultures tended to live in a very spiritual and "living" landscape (each individual tree or rock might have a spirit), early people were on the lookout for signs that would explain the day to day world around them. Some objects, like rocks and water, might have visible manifestations but show very little activity or change over the course of a season, so have very "limited spirits". The river god periodically flexes his muscles and floods the land, but then goes to sleep for the summer.
Totemic animals would be the ones which could provide a range of fascinating activities to the observant hunter gatherer or early farmer, and these actions would then be "mapped" onto the mental picture of the universe. Gifted story tellers could take these observations and "mappings" to explain the wider world in ways that people would understand (i.e. while the river god is sleeping, the crows are flying into the fields to steal his grain).
Obviously the more "primitive" the world view and the more that things are explained by animating spirits, the more elaborate and disconnected from "reality" some of thee myths could become. As societies became more "rational" and people observed there were actual causes and effects (and needed less of a spiritual explanation to how things worked), then the meaning of animals would become more "literal". The ancient Romans observed the Eagle was a powerful predator and associated it with the god Jupiter. Americans, living in the Age of Enlightenment, could still take the Eagle as a symbol of power as a predator, without necessarily evoking a deity to explain it. Modern sports teams still do this sort of thing today (The Toronto "Raptors", or the Denver "Broncos", for example).
So depending on the "time" of your story setting, the people can be using the animal as a symbol for a spiritual being to explain how the world works or evoke the animal for qualities that the people would like to emulate.
An interesting one in Australia is the Rainbow Serpent responsible for creating much of the landscape.
When you fly over Australia - or I presume stand on a high hill or mountain you can see in the land below great crescent shaped marks filled with water that are just like the marks some snakes make when they "shoulder" their way across sand.
Now the geology is that these marks are made when rivers and streams change course and the deeper pools at the bends where the water ran faster remain long after the river moved on.
But from an Aboriginal perspective it makes a great story to imagine a huge snake - the rainbow serpent - moving across the land and making the features of the landscape.
So to answer your question in your landscape you have features - rivers, rock formations, mountains whose shape is similar in some way to an animal or the marks that an animal makes and build a story around this.
Perhaps winds through a cave system sounds just like the roar of a lion and evolve a myth that a mighty lion died in the cave and his spirit lives there to this day.
The thing is that when people see the landscape they must see the "truth" of the tale. They can see the marks of the serpent, they can see the jumble of rocks where the giants had their battle, they can hear the roar of the lion.
The question has two parts, which I will address separately.
Most myths and legends begin, when a group of people are sitting around campfire, in a cave, or in a hut... Outside Mother Nature unleashes her fury, by sending torrents of rain and casting roaring thunders. Wind slams against the walls, yet in the middle of the darkness you think that you saw something. A movement maybe? Or was it a pair of eyes, full of hunger and hate?
Before you can ask the guy next to you if he saw the same thing, the oldest man in the room, an experienced hunter and brave warrior, begins his tale...
Have I ever told you, how I lost my middle finger? No? Well then, you see, wolves have a very peculiar habit...
If you want to create a good myth, imagine yourself sitting in such hut, hungry and thirsty, listening to old man, looking at his scarred face, while he tries to scare the shit out of you and comfort you at the same time.
And now fast-forward 50 years. You are now the elder, perhaps you are missing a limb or an eye. All eyes are fixed on you, waiting impatiently for words of of wisdom. You take a deep breath, take a sip from your cup and start retelling the same story you've heard so long ago in a lonely hut. Sometimes you omit something, sometime you add something from yourself, but one way of the other it's still the same story about peculiar habit of the wolves.
If you want to create myths, put yourself in this mindset, and you shall not err.
One way or the other - fear. Fear comes in different shapes and forms.
Some are afraid, that they will meet a giant bear, while hiking in the woods. So they build little shrines, so the spirits of the forest will divert the bear from their path. Others know how to use that fear - they dress up as bears to strike destroy courage of their enemies, or they hunt for the huge animals to gain respect of their tribe.
Bears are fearsome, because they are big, strong and hard to kill, and those qualities are recognized in bear-related myths.
Some are afraid, that a pack of wolves will attack their cattle, and they will watch helplessly, as their food supply is destroyed before they very eyes. So they build little shrines, to divert wolves to the next valley. Others know, how to use that fear - they mimic a pack of wolves while attacking an enemy, to make an impression of one, perfectly coordinated killing machine.
Wolves are fearsome, because they are excellent trackers, they have strong jaws and sharp claws, and they can work as a team. Those qualities are recognized in wolf-related myths.
Some are afraid, that a fox will sneak into their farm and kill all the chickens and they will starve. So they fortify their henhouses hoping to stop the animal.
Foxes are fearsome, because they are smart and agile. Those qualities are recognized in fox-related myths.
Some are afraid, that their cattle will fall victim to a disease and die, or that they will not reproduce.
Some are afraid, that rats will infest their pantry.
Some are afraid, that a certain species of bird will not make its nest on the roof, which is a sign of bad luck.
We can go on like this forever, but I think you get the idea. Think of an animal, connect some sort of fear to it and turn it into a story.
