The basic deity descriptions in the Pathfinder Roleplaying Game are very basic indeed. Name, alignment, domains (and later, subdomains) assigned, and favored weapon.
Some deities have expanded descriptions, needed to support some feats and prestige classes that grant power (including spell-like abilities) in exchange for performing obediences, ritualistic activities done each day.
Where a cleric has a relatively generic ‘prayer time’ each day, the obediences spell out the activities required. This is almost entirely descriptive, though in some cases the descriptions suggest some significant effort is needed. Like a cleric’s prayers or a wizard’s spell preparation, there is little mechanical effect, they’re an explanation for the powers gained.
This is good enough for me, and I think I’d be happy to see clerics replace the generic prayers with their deities’ obediences.
For Divine Trappings, this means I will probably include some elements that could be included in an obedience. A deity of Air might be looking for some kind special incense, or music of wind instruments (or of drums, signifying thunder), or a multitude of pretty fans or wind chimes that need to be set up as part of the obedience. There might be different requirements when traveling and when not — a follower of this deity might have wind chimes always set up near their obedience location, while part of the obedience of a travelling follower might be to assemble something similar from found materials, then leave it behind.
The covenants section of Classic Play: Book of Immortals has some elements that could be used. I expect to mostly use this section to develop dogmas, tenets, and duties, but the obediences could have ritualistic or symbolic elements related to these.
Research for my previous post on naming deities resulted in me rereading my Patrons of Low Fantasy series… to my surprise, while I do have some information there about gaining and using favor, I had nothing that would directly apply to obediences. As above, some elements that could be ritualized or treated symbolically, but nothing directly applicable. This feels reasonable to me, though: the patrons aren’t looking for worship, they’re looking for agents and those willing to exchange specific service or service toward specific goals, for power.
So. For domain aspects, I should look at what sorts of activities and actions could be appropriate to each domain.