Lake Itasca, at the source of the Mississippi River
The Crow call themselves the Apsáalooke, the Bird's Children; Crow is an English translation of Apsáalooke. Around 500 AD the Crow people seem to have been living around the sources of the Mississippi river in Wisconsin or Minnesota, as part of the Hidatsa people, who spoke a language related to Sioux. The Crow were east of the Cheyenne and a little further west than the Mandan, and like both the Cheyenne and the Mandan the Crow people were farmers, growing tobacco as well as corn, squash, sunflowers, and beans. Crow people lived in earth lodges, with several families in each lodge.
Possibly around 1000 AD, when a global warming period made the Sioux push the Mandan further west, the Mandan pushed the Crow further west as well, into what is now North and South Dakota. Like the Mandan, the Crow people kept on farming in the Dakotas, but now they began to hunt buffalo a little too. Crow people had many dogs and used them to pull travois (sleds) as well as to help in hunting.
Learn by doing: eat some sunflower seeds
Later Crow history