The Sun Goddess of Arinna
I will note that there is not a lot out there that I can find on her in English, but I'll like to the few encyclopedias that mention her at the bottom.
The Sun Goddess of Arinna was the chief goddess of the Hittite religion and, as her name suggests, her major cult center was in the city of Arinna, outside of Hattusa (Hittite capital). She is the consort of the god Tarhunna. She legitimized the authority of the king, who was considered to be her priest.
The king would honor her with prayers every day at sun down.
Names
Her names are as follows:
- Ištanu(1)
- Eštan(1)
- Wurunšemu, "Mother of the land"
- Arinitti, "The Arinnian"
- Arinniti (unsure if this is just an alternate spelling or if there's a difference I'm not privy to)
- 𒀭𒌓 (Sumerogram, d'UTU, meaning sun god)
Depictions
She was depicted as a solar disc or as a woman, seated, with a halo.
Other Historical Information
Apple trees are mentioned in a myth fragment. It also seems like deer were sacred to her and that her messanger was an eagle.
Modern Worship
My ideas regarding how to worship her in the modern day would be to incorporate solar imagery on your altar and/or devotional items. It might also be a nice idea to enjoy sunny days outside. As the most important deity in the pantheon, you could also dedicate learning about Hittite religion and culture to her, or reading what you can find about Hittite mythology. Depictions of deer on your altar would be a good idea for her, as well.
As far as offerings, I'd go with your gut on this one. Maybe use the myth fragment as a hint and offer her apples (or any derivative of, such as cider). Given her status, it might be nice to offer her things you personally feel are of particularly high quality or importance.
Notes
(1) These names may actually refer to the Sun God of the Heavens