To start with, the aim for the first year of teaching at any level is just to be clear and organized. Set the expectations low for yourself--don't try to flip a classroom if you have never done it, don't build in elaborate simulations unless you have done it before or can borrow from those for whom you have TA'ed, don't aim to be wildly funny or entertaining. The first year means lots of new course preparations, which involve a lot of work. Get them right and you have the foundation for teaching for, um, much of the rest of your career. Sure, you will teach new classes and teach the old ones in different ways, but the frameworks you set up will be useful far down the road.
A fundamental rule, unless one has TA's and one does not usually have a teaching assistant for a grad class, is that whatever you assign, you have to do--read or grade or whatever.
Borrow what you can--use the syllabi of classes you took as inspiration--either to do or to avoid depending on what you thought of the class. I was lucky to TA for the same class three times in my second year in grad school--it was taught well, it was taught poorly, and it was taught ... experimentally (the Cold War was ending). So, I borrowed heavily from the former, a bit from the latter, and avoided what the less good prof did.
Figure out what the norms are of your department--what are normal office hours, how much reading is generally assigned, what is the normal kind of assignment load. You want to be somewhere near the department norms as much for student expectations as for fitting in. Over time, you can deviate, but best not to shake things up at the start.
Why such a conservative start? Because the first year is really hard as you will be doing not one new job but several--teaching new classes to new students, researching beyond the dissertation, doing much service to the department/university/profession, public engagement, mentoring, etc. It is a lot, and it can be very stressful when combined to living in a new place, figuring out who you can trust in your new situation, and all the rest.
Some other random bits of advice for the person starting out:
- Be kind to staff--many faculty are not. But they work harder and don't have the freedom that profs have to control what they do.
- Figure out your rhythm--when you write better, when you read better--and build your office hours and other obligations around your rhythm so that you can try to be productive. It is really hard to work on one's research during one's first year of teaching, so don't expect too much, but build your schedule as best as you can to facilitate it. That might mean carving out mornings or carving out one or two days a week. Whatever works for you.
- Get a sense of the culture--does everybody come in every day or do folks stay home on non-teaching days (this is mostly a post-pandemic question)? Do people eat lunch together?
- Ask your chair about service expectations and see if there is a culture for protecting junior faculty from doing too much service (there should be). Beware that if you are not a straight white guy, you may be asked to do more service to represent those who have been historically excluded, and that is a real problem since the few get hit with a lot of work, making it hard to progress.
Which leads to the big bit of advice. It is ok to say no. Not to everything, not all the time, but be strategic and say no to the things that are huge time sucks that don't advance your career. Few folks get new jobs or tenure due to great service. You should contribute to the greater good, but do so in ways that inform you about your new place and don't involve too much work. This means identifying some people in the department who can be straight with you about what is and is not onerous.
It has been a long, long time since I started prof-ing. I have forgotten much, so any suggestions by others would be most welcome. The good news is that my big day one mistake is one you are unlikely to make: I forgot to bring the copies of the syllabus to the first class on my first day .. and then to my second class on my first day ... and then to my third class on my first day. These days, that stuff is all online. So, enjoy whatever your first mistake is--you will remember it, but damn few others will unless you blog about it repeatedly.