All details should be decided and agreed to ahead of time.
An important consideration is who gets to shoot. A lot of trips have been ruined over this. If two are together, it is common for who sees it shoots it. But this is entirely unsatisfactory, because the game is usually seen by both parties, about the same time.
A system I worked out is by time. Starting out in the morning, prime time, agree on fifteen minute time period for a shooter. Flip to see who gets first time period and during that time period any game seen is shot by the designated party. In fifteen minutes you change shooters. I have never seen a problem with this plan.
In some groups where hunters are alone from each other, first hunter to see game fills all tags, if he can. I will have no part of this. If I think there is the slightest chance that one person my do this, I make it crystal clear ahead of time. My tag is my tag and no one else can use it. The first time I went with a well known hunter and told him this, he couldn't believe what he was hearing, but I wouldn't give. He said what if he accidentally shot two moose? Looks like you would have a problem, doesn't it?
No problem can arise, if everything is clear ahead of time.