For those of you unaware of her name or purpose, she is a Hellenic goddess associated with strength of will, the hunt, ritual purity, as the mother/mistress of all animals, and as a goddess of the Moon. There are times, too, where she is seen as a kind of Vengeful Virgin, as we see in the story when Actaeon saw her bathing in the buff.
As the story goes, she turned him into a stag and set his hounds against him, killing two birds with one stone.
We can see through stories such as these that she's quite protective of her image, but also of those who have been hurt or harmed by another. She can be invoked by those who have been bullied by others, by those who have been backed into a corner, and by those who need help finding direction in their lives after a traumatic event.
To do so, I would recommend that you procure Dittany of Crete, macerate it in a mortar and pestle, then set it on a hot coal for her. Following this, say the Orphic Hymn to honor and invoke her:
"Hear me, Jove's daughter, celebrated queen, Bacchian and Titan, of a noble mien:
In darts rejoicing and on all to shine, torch-bearing Goddess, Dictynna divine;
O'er births presiding, and thyself a maid, to labour-pangs imparting ready aid:
Dissolver of the zone and wrinkl'd care, fierce huntress, glorying in the Sylvan war:
Swift in the course, in dreadful arrows skill'd, wandering by night, rejoicing in the field:
Of manly form, erect, of bounteous mind, illustrious dæmon, nurse of human kind:
Immortal, earthly, bane of monsters fell, 'tis thine; blest maid, on woody hills to dwell:
Foe of the stag, whom woods and dogs delight, in endless youth who flourish fair and bright.
O, universal queen, august, divine, a various form, Cydonian pow'r, is thine:
Dread guardian Goddess, with benignant mind auspicious, come to mystic rites inclin'd
Give earth a store of beauteous fruits to bear, send gentle Peace, and Health with lovely hair,
And to the mountains drive Disease and Care."
When you've completed the oration, speak Artemis' name and tell her what it is you seek. Light a candle for her and watch the smoke off the coal & the candle's flame for indications of her interest or willingness.
As you are speaking these words and performing this ritual, it is very likely that you will feel a little odd. These rites have a way of inspiring substantial change, and that is as intended.
Note: Credit for the invocation goes to Theoi.com.