First off, welcome!!!
I know it may sound like MsMarieh isn't being real helpful, but we tend to try to be quite specific in our help on here. If you are needing just general suggestions on how to be a good admin, I'm sure we could all put our $0.02 in, but if they don't apply to your field, then that information wasn't helpful at all.
As a new Admin, I would say first thing, give yourself time to learn the office and what works and doesn't work for you. Talk to your supervisor about expectations that they have for you, and what freedom they are offering you in your position regarding changes you can make without authorization. If there is a SOP binder for your job, I'd take it home and study it. If not, while you're learning is a great time to make one. Starts with important contact numbers you need to know, what duties are expected (and when!), etc. I mean, you don't wanna learn that you're supposed to make coffee for a board meeting the 3rd Wed of the month on the day you're supposed to be making the coffee!

These are probably things you've already thought of... but like MsMarieh said, the more details you give us, the more exact suggestions we can make! Welcome to our community!!!!