Having been in similar shoes not that long ago...
While my college does have a "Student Stage Management Guide," it is essentially a Word document that has all of the text and most of the diagrams you can find in one of the published books on SM - because the Head of Production wrote it. Very helpful (and hey, it's not a cheap book, so the free copy is welcome!!) but 180 pages isn't too welcoming, especially when you've just finished rehearsal, and need to know NOW how to handle a given issue.
Looking back at my first year, I would say that a department cheat sheet would be a great first step - a simple breakdown of who deals with what. A table listing each shop/department head, their email and phone, office/room, and a brief description of what areas they handle. Under department heads, list any assistants. For instance: the costume shop is going to handle building or renting garments; who is the cutter/draper? Who is the stock manager? Who will be on the dresser crew for the show? Is there a person in the shop who deal with anything exclusively - dyeing, renting, etc?
This list would take some time, and probably a good long talk with a production manager or director, to put together, but I imagine it might help.
You could also keep a show journal - document what you've done at the end of each day or week, and include brief notes on whether it was timely, last-minute, etc. I tend to dedicate the last page of my current notepad to "next time I'll do it like this" notes - everything from the layout of the sign-in sheet to snacks for tech to how to call breaks.
Hope this helps - it's wonderful that you are helping to lay a foundation for your classmates and future students. Best of luck.
Meg