This one appears to be a guide for shamans who need to collaborate with priests from other temples who worship different gods! 

Ooh, how do they do that and why?

Well, it seems like in some situations (historical cases given: a plague, a severe multi-year drought across an entire region, a barley-blight that hit crops heavily across many towns), the Star-Eyed can't intervene to help just with Her own resources, and the advice given by the avatars to the shamans is to seek alliance with other faiths. Or, sometimes, the priests of other temples are the ones to reach out to theirs. 

In terms of the how: there are a lot of suggestions given by the book's author for scripts to use, though they seem to be somewhat culturally-specific and the books is three hundred years old and by an author who lived well south of Tantara's borders, before the time when most of the Kaled'a'in tribes chose to move to Tantara.

The advice given for when to consult a spirit avatar is maybe more generalizable. The priests of other temples might be venal and want to extract political concessions from the Kaled'a'in people before they agree to pray to their god as well! If that happens you should talk to a spirit avatar about it! And here is a long list of additional scenarios that could happen and where the Goddess is willing and in fact would want to directly provide input through Her intermediaries! 

How did they get a list of situations in which to call oh her? Did she supply it or did they guess and check?

The book does not make this totally clear! 

It mostly sounds like the shamans would talk to spirit avatars for advice in a lot of situations, including less-dire ones where the Goddess either didn't think it was worth personally intervening at all, or did but could fix it Herself with a miracle or two. The list here is curated from past times when neither of these was enough. 

Aza reads the whole book and takes plenty of notes organized so she won't mind showing Ma'ar.

Ma’ar Mindtouches her around lunchtime the next day; he’s done reading both of the books he took and has notes, maybe they can plan to quickly exchange and catch up on those before they visit the shaman?

Sounds good to her!

Ma'ar meets her at the appointed time, and hands her a sheaf of notes. 

"The two I had were about the history of religious disputes between different factions of the Kaled'a'in people over their history, and about the spirit world. Yours?" 

"Stuff on collaborating between different churches." Note trade!

Going by Ma'ar's notes, the Kaled'a'in have had fewer and less stupid internal disputes over their history than the war mentioned with the two factions worshipping the Twain; their doctrine seems to be broader, more allowing of variations in local worship, and the spirit avatars usually resolve succession disagreements. The disputes that managed to happen anyway were mostly between rather than within clans, sometimes over territory and only incidentally religious in nature; once a family feud managed to last for an entire generation before the shamans got fed up with it enough to get spirit avatar advice on it. On a couple of occasions, people have impersonated shamans and faked advice from the spirit avatars, and only been found out after months or years of this. 

"I wonder how people first got the idea of worshiping gods," Aza remarks, as she pages through. "If you didn't already have them, wouldn't they seem weird? Especially since they can barely talk."

"I don't know! That is pretty weird." 

Ma'ar's notes about the spirit world are less useful, apparently the book was very vague. There are legends about various dangerous monsters there; it's hard to tell, Ma'ar adds in the margin, whether they're anything more than just legendary. There is a lot of advice which is hard to interpret in the absence of ever having been there.

"Maybe there are lots that don't try to talk," she speculates, "so nobody knows about them, and we only see the tip of the iceberg."

"Huh. Interesting thought." He glances up from reading her notes. "You ready to go in now?" 

"Sure."

Someone ushers them into the temple, again, and to Summerhawk's little office. 

She does not seem as pleased to see them this time. 

Ma'ar had been going to ask questions but now he's back to being kind of scared. 

"...hi, how are you? If this is a bad time we can come by some other day."

"No, the time is fine." She stands up. "I spoke to the senior shaman and he spoke to one of Her avatars, and - they did not think it appropriate for us to invite you to the Moonpaths, when you are neither Kaled'a'in nor Her worshippers at all." 

"Oh, I'm sorry to hear that." She starts unpacking the books they're returning.

The shaman thanks her and goes to put them away. "Did you have any other questions while you are here." 

"Is - something bothering you?"

"No? I am not displeased by your questions or anything, it was a pleasure to answer them." 

Ma'ar is VERY DUBIOUS of this claim but says nothing and also doesn't read her mind to check if he's right.