(UGH I’M AN IDIOT AND PUBLISHED THE ORIGINAL ASK BEFORE TYPING EVERYTHING. So sorry!)
Anyway… I haven’t worked with Midna yet, so I can’t tell you a sure-fire way. However, I just finished replaying Twilight Princess so details about her are fresh in my mind (and in my heart ♥)
—>WARNING: HUGE SPOILERS FOR TWILIGHT PRINCESS.<—
My first instinct is that you should probably incorporate the Mirror of Twilight:
Considering this Mirror is paramount to communicating with the Twilight Realm. You could either print out this design or perhaps try to enchant a mirror for that purpose. Be careful, since the Mirror has immense powers. (That’s why Midna destroys it at the end of the game for that reason.)
Midna is also part of the Twili, so reading up on that race would help to get background on her native culture. (Sources on Twili: x, x, x.) A huge thing to keep in mind is light. Midna and other Twili get sick when exposed to large amounts of light, so calling on Midna at twilight (dusk or dawn) or in the darker evening would most likely be best.
Also, perhaps trying to use a Twilight Portal would help, since that is how the Twili seem to navigate around the world:
And while I don’t have a specific ritual in mind or ritual structure you could use, I do like this article, “To Give Offerings to a New and Welcomed Spirit.” I’m thinking that instead of a shrine, using the Mirror of Twilight or a Twilight Portal would be better. My personal rules about hospitality dictate giving an offering to a spirit—especially a new one—but I don’t know exactly what Midna would like. I’m feeling she might like apples or something very “earthy” since it would be something she couldn’t get in the Twilight Realm.
Ooh, an idea that I got from varmafre’s ritual with Farore is to play Midna’s theme during the ritual.
Sorry this is rambling and disjointed. I haven’t yet tried to contact any LoZ entity yet, so I’m terribly inexperience.
Followers! PC Pagans! Any other advice?