Summoner don’ts!

Don’t die! The host should be somewhat defensive and smart about how they fight. Summoning takes time and it is really annoying to take the time to join someone’s world just to have them die to something stupid. It is going to happen but paying attention to your health and the circumstances to ensure you stay alive will help everyone get the most out of the session.
Don’t summon someone and then run off. You should wait for them to show up and direct them by leading the way.
Don’t summon someone for a Chariot dungeon until after you have destroyed the chariot/s. The three chariot dungeons are a pain in the ass for groups. They are designed as puzzles to solve by memorizing the safe routes and strategies to get to the point where you can destroy the chariots and make your way through to the boss without the chariots in the way. The whole point of co-op is to help the host with enemies. The chariots are not an enemy, they are a puzzle and a group will just get damaged and the host might die along the way so that it becomes a waste of time for the summons and even if you make it to the boss you are diminished and less likely to win the boss fight making it a waste of time again.
Don’t fight a boss if your summon is out of HP. If it was a hard road to the boss and your summon is out of HP or flasks or both then just dismiss them and go get another summon or fight the boss with the other summon that is healthy. For every summon the boss gets harder so having a summon that will die soon into the fight makes it harder on the others and makes it less likely they will win.

Split the difference!

There are two main reasons to summon someone: Plus a bonus reason.

Explore the area and make your way to the boss. If they want to fight the enemies in the area they should start to do that right away to tell the summon/s what they want them to help with. If the host just starts to run to the boss the summon/s should not waste time and resources fighting the enemies unless they pose a threat to getting to the boss or killing the host.
To kill the boss. If the host starts running through the area toward the boss then the summons should just follow and be prepared to fight the boss. It is usually not a good idea for the host to try to search the area, kill enemies and kill the boss in one go-through. Bosses are better to fight fresh and with maximal resources. It is better to split the area into two parts so if you want to search the area then do that with help, dismiss the summons, rest at the site of grace and then resummon for the boss. This allows all involved a higher likelihood of surviving and getting runes without wasting time dying or the host dying.
Another reason to summon is to get a specific item or solve a puzzle that involves killing a tough but non-boss enemy. This might involve just helping the host get somewhere tough in the area or retrieve their runes. They might just run there and want some backup or they might want to fight their way to the item or location. In this case, the summon should try to protect the host as much as possible and help them get to their goal. It’s called jolly cooperation for a reason. The summon is there to serve the host’s goals not the other way around.

Summonee Don’ts!

Don’t Die.
Don’t run off.
Don’t let the host die. If the host dies it’s all over. No one gets any more runes and everyone has to start over. This is especially true during a boss fight. I hate it when I summon someone during a fight and they don’t take any aggro. A summon should sacrifice themself a little bit in order for the host to stay alive. This means taking turns fighting or taking aggro so the host can heal. This can be done from range as well if the summon is low on health or flasks or is to far from the enemy. If there are multiple enemies take aggro from one so the host can fight one on one. If the host is staggered try to get a hit in to give them a chance to recover.
Don’t get in the way or cause a fall. Stay out of the way in tight spaces and don’t block doorways or hallways. Let the host retreat and keep moving if in a narrow area. If you are jumping up or down get out of the way so the host can jump where you are and not fall back or down. Also, keep a little distance sometimes so that if there is an ambush or big enemy you don’t both get hit.

5. Don’t mess up a sneaky move. There are lots of ways to cheese enemies and sometimes it is better to sneak up than to just smash your way through an enemy or group of enemies. The host should crouch to indicate that they want to do something stealthy and then the summonee should also crouch and get behind the host to not aggro any of the enemies before the host makes their move. Ruining someone’s clever strategy is annoying and usually will cost resources or lead to death. If the host wants to sneak up and poison someone from behind then let them do it so that everyone wins.