There are differences among the myths of different tribes, but there are many similarities.
There are probably several turtle stories. The one I know is a Lakota story known as an "Earth Diver" myth. It is a common theme in
Native American myth.
Briefly, a maiden lived in heaven with her tribe, but one day fell out of heaven and into the ocean.
She befriended a turtle and a few other animals. She asked the animals if any can travel down to the bottom of the ocean to
sea if they can find some mud. In one version, the frog was successful. He only had a bit of mud in his mouth, but that was all she needed.
She proceeded to spread the mud on the turtle's back until she formed the earth.
To this day, the turtle supports the world.
I have been reading a lot about it lately. The turtle is a very important symbol. It does represent Mother Earth. I never knew there was so much symbolism for such an unassuming animal.
There are some native american doulas that take the Turtle as their spirit guide. Here is how one of them explains it:
The turtle is a totem animal in Native American culture. The grandmothers and grandfathers spoke of the turtle as a symbol of mother earth and female strength. The turtle was respected for its qualities of nurturance, protection, patience, perseverance, tenacity, self-reliance, groundedness, and wisdom. The turtle teaches us that we blossom in our own time and that we must go within to find the answers that we seek.
It seems talking/sentient animals are a very common theme in Native myths. That may seem like a silly observation to make, but talking animals seem to be much rarer in most other continents' traditions.
In fairy tales, there is almost always a sentient animal of some sort, though very rarely talking. In fact I can only think of one tale offhand in which an animal talks ("East of the Sun, West of the Moon", Asbjørnsen and Moe -- the white bear).