I like to honor Artemis during the deer hunting season which begins in late September or as the Sun enters Sagittarius in November, when deer hunting is in full swing. The new moon in either Sagittarius or Scorpio are also appropriate times.

You will need:

2 candles placed in the center of your kitchen table
Incense (pref frankincense)
Olive oil
Salt
Bread
A glass of wine or juice
Offering dish

Decorate the altar (i.e. The kitchen table) with symbols of Artemis. Images of Her, bow and arrow, bear, stag, hind.

Begin by washing your hands with soap and water or with a salt or sugar scrub.

Light the incense. Asperge the area and yourself. Set the incense back on the altar and let it continue to burn.

Light the first candle:
"Hestia, first and last I honor you."

Light the second candle:
"Artemis, I come before you this your holy day in joy and thankfulness."

Recite a prayer to Artemis, either freeform of the Orphic Hymn to Artemis or the Homeric Hymn to Artemis.

List the blessings you have received from Artemis in the past year and talk about the challenges in the coming year. Present offerings.

Libations:

"Hestia, in thanks for this hearth at which I may worship all the Gods, I pour out this libation first to you."

"Artemis, in thanks for your many gifts, as I have just related, I pour out this libation to you."

Drink the rest saying: "By the will of the Gods, I have this wine/juice that I need not know thirst."

Feast:
Take the bread and dip it in olive oil and sprinkle it with salt. Place a bit in the libation bowl or offering dish and eat the rest.
"By the will of the Gods, I have food to fill my belly that I need not know hunger."

Closing:

"Artemis, I thank you for hearing my prayer." Snuff out the second candle.

"Hestia, I honor you first and last." Snuff out the first candle.

Put out the incense and take the water, the libation and the offering outside.