Listen, then correct
The single greatest tip here is to emulate Shog9, a former Community Manager. Seriously, there's no better example of what a Community Manager should strive to be. Shog9's greatest strength was getting people aspire to be better. From various posts in that question
At times I've been at my worst and he was the only one able to see the good in me. He helped me very much before I was hired, when I was at Stack and even after.
You taught me how to conduct myself in a written form. You taught me how to convey compassion and empathy. You taught me the value of a subtle take. You taught me how to help open minds to change without trying to bend them to my will.
A lot of the residual "political" anger happened when people felt they were no longer heard. Shog9 would listen and then correct. The key is to strike that balance. Listening to the community is always important, while sometimes telling people what they don't want to hear at the time. There's going to be times you will be stuck between your employer and the community. It won't be easy or popular, but as long as people feel like you have their best interests at heart, you'll pull through.
Do some moderation
You now have a diamond on every SE site (literally), in addition to a whole host of special tooling. Maybe you have some experience with a diamond, but you might just as likely be completely new to using the tools moderators use. It's worth your time to explore those powers for two reasons
- You're interacting with moderators and understanding where they're coming from is helpful to both you and them
- You need to know how the tooling is actually used in practice. There are times that CMs (who don't use the "regular" mod tools) forget functionality or even miss it's there (did you know you can edit-ban low rep users? The interface kinda hides that)
There are some userscripts you'll want as well. Check out the Moderation Team for a list. Jump into moderator chat rooms if you have questions.
Do some normal-user review queues as well (and remember Stack Overflow also has the unique Triage and Help and Improvement queues)
Chat some
Chat is rarely formal and there's no shortage of places to interact with users. In addition to Teacher's Lounge and the various mod-only chat rooms, there are some sub-project rooms run by normal users. Places to visit include
- Tavern on the Meta - Meta Stack Exchange General chit-chat (often has CMs)
- SOBotics - The inverse of Tavern in that there's very little chit-chat, but you can see the efforts the community has put into helping the moderation effort
- SO Close Vote Reviewers - A group of people dedicated to site cleanup (SO only)
- Charcoal - Community anti-spam project
Remember that there's three chat servers (SO, SE and MSE), and only SE overlaps in moderation.