Well, it probably wouldn't hurt to look at Azura as a deity herself. She boasts wisdom and may be seem as one of the more benevolent daedra(if not a bit vain and egotistical) but a daedra she still is, just as well known for her potential cruelty and ominous frequency to how she always gets her way.
There aren't really a whole lot in detail about her specific worship, especially with that of the dunmer/chimer >_> since she plays a large part in their cultural origins.. Which also shouldn't be too surprising since she seems more interested in the mortal affairs of her worshippers than most Princes(Hence why she's probably popular to the masses) The Tribunal in morrowind only seem to complicate this already mix-mash of a pantheon
As per actual tenets, and the more finer details.. We frankly just don't know. It's still vague and not something commonly explored. Though, I would imagine different cultures/races have different criteria >_> the Dunmer for one, have a long, long history with her. Plus.. Ya know.. Their egotistical and cruel as well.. Hard to say if that's an elf thing or a daedra thing
But ya, to get straight to the answer, you probably would be fine just having your cleric invoke her name and that of the Tribunal(given the time setting), along with portraying a more wise, knowledgeable persona.. Or at least venerating of said qualities(i.e scholar) It's also up to you if you wanna be more fanatical about it, but it's not necessary, especially for a dunmer
But for real though, playing as an Ashlander/Old Tradition's Cleric has it's charms. Is it different than your typical Dunmer paying respects to their ancestral god? Most likely. But hey, it's D&D session, why sweat the smaller details when you can have fun (And for the record, an Orc Bard is the best bard)