(Caveat: What is agreed must be reasonable, considering system and genre.)
Rule Two: All involved should adhere to Wheaton's Law ("Don't be a dick".)
(Corollary to Wheaton's Law: your character can be a dick as long you, the player, are not being a dick.)
If tensions arise then everyone should invoke the Modified MST3K Mantra ("It's just a game, I should really just relax.")
Totals are calculated by number of cards in the most relevant domain, + 1 for your element (if it is appropriate), + 1 for your animal (if one or more of your animal traits are appropriate).
Nearby characters who are interested can add their relevant domain cards to either side if they wish.
Minor complications like surprise, darkness, terrain, etc are ignored in contests between Gods.
Players may roll a dice to add the result to their total (++, +, 0, -, --).
Higher total Succeeds. Success is Yes/No. There are no levels of success. Ties favour the defender.
It is a turn based system, All actions are mechanically simultaneous. Each turn Players get one action, and get to resist any actions taken against them. There is no penalty for defending against multiple attackers. If two characters are in conflict, both declare their intended actions, and both actions get mechanically resolved, before either gets narrated as actually happening.
For GM convenience each turn against NPCs is broken into three phases:- (1) NPC's intent, (2) Player's intent and (3) Narrate Result. Repeat as needed.
Example: Two New Gods (Athena and Bast) are in a conflict to determine the outcome of a naval battle between mortals. Athena has 6 war domain cards, but their element and animal traits are not appropriate, giving them a total of 6. Bast has 4 ocean cards, the water element, and can apply the "cunning" trait of their animal which gives them a total of 6. Cylwin see what is happening and offers to help Athena with their one war card (Cylwin's animal and elements don't get counted). Bast decides to roll a die in an attempt to win, and unfortunately gets a "-". The final totals are Athena 7 and Bast 5. Athena gets to decide the outcome of the naval battle.