Obviously you should always treat those around you with respect. Here are some tips for collaborating with some of the different people you'll work with.
Get to know the strengths and weaknesses of your team. You want everyone to get a chance to try different tasks, but is someone really good at tracks and terrible at blocking? Let them focus on tracks. Try to highlight people's strengths––you want them to enjoy being there.
A strong team is one that knows each other well and gets along. Establish your team group chat early and try to get to know each person individually. You'll be spending a TON of time together over the next few months so if everyone is fighting, it will quickly become a terrible experience.
Always treat your team as equals––although part of their job is helping you out, you are all stage managers, and more importantly, you are a team.
Delegating tasks will also be a huge part of your job, which is why it's so important to know who excels at which types of jobs. It's good to have a well-rounded team of people who like each other and, between each of them, cover all your bases of types of tasks (e.g. paperwork, understanding tech, understanding tracks, other areas).
You need to gain the respect of the cast from the beginning so that when it gets to be crunch time, you know they'll listen. NEVER try to "assert dominance" or anything like that over the cast. You will get much farther by treating them with kindness, while at the same time making it clear that they do need to listen.
Little symbolic gestures can actually go along way to establish respect between you and the cast. Although these kinds of things may seem unimportant (and on the surface level, they are), the cast will take note and it will shape the way they interact with you throughout the show process.
You should also be consistent! Don't tell everyone to be quiet and then turn to the people around you and make fun of yourself for saying it. Take yourself seriously.
Another important part of gaining their respect is making sure they understand what you do. Some people don't know what an SM is––show them.
For the most part, besides meetings, you will not see the designers frequently. That's why it's important to have an active BAND chat and always distribute rehearsal reports in a timely manner.
Designers should feel comfortable asking you questions and you should always ask them to confirm receipt––if you're just sending things out and never getting anything back from them, that's not helping anyone. Remember to be polite and communicate with them frequently so they don't feel out of the loop.
During the show, you will also work with run crew. Try to always go to the right person for the job when you need help with something; it's a way to show that you respect what they do. Don't go over their heads and just pull random people––their time is just as important as yours.