Artemis was widely known as the goddess of wilderness and the hunt. Outside of the cities, this was her primary aspect as she governed not only animals and the hunt, but also fishing, springs, and forest fires. Her identification with wild things, however, also had great, if indirect, bearing on how she was perceived and approached as a deity.
In terms of everyday worship, Artemis was a life-cycle goddess. She was far more likely to be called upon with regard to matters of birth, marriage, and death, all rites of passage. Women in childbirth called on her to ease their suffering* and all infants were under her protection. Boys passed into her brother Apollo’s responsibility as soon as they were weaned, but girls remained under her care until they wed. Young Athenian women, at least those of a certain class, were sent to Brauron to be her priestesses** and girls all over Greece sacrificed to her as part of their passage from childhood to marriage and adulthood. In Gortyn, a woman wishing to absolve herself of an accusation of theft on her divorce was required to swear before Artemis that she had not done so.
There was, however, a dark side to her care. A woman who died suddenly for any reason, but especially in childbirth or of plague was said to have been shot by Artemis. The death of any girl-child was also laid at her feet. Artemis Orthia of Sparta was said to require human blood, acquired through the tradition of scourging boys. This was also where her wild side came in. She was not an orderly goddess and she was swift in her retribution. There are more stories of her anger than of her favour and while she protected, she was also one to be feared.
*She was also sometimes identified with Eileithiya, goddess of childbirth.
**This was called “playing the bear,” and its purpose was to appease the goddess. According to myth, some young men had killed a bear for scratching their sister after she provoked it. Artemis sent a plague to Athens until they began this practice of sending their daughters as her priestesses.
A prayer to Artemis, AP VI.273, found in Lefkowitz & Fant, Women's Life in Greece and Rome - Google Books
Law Code of Gortyn - Diotima
Alkman 1.5-101 - Diotima
Pausanias, Description of Greece 3.16.7-17.2 - Perseus
Artemis - Theoi (This site gives a whole lot more primary sources. And it's really cool in general)
Pomeroy, Sarah B. Goddesses, Whores, Wives, and Slaves. New York: Schocken, 1995.
Pomeroy, Sarah B. Spartan Women. New York: Oxford University Press, 2002.
Artemis - Wikipedia
Sanctuary of Artemis Orthia - Wikipedia
Cult of Artemis at Brauron - Wikipedia