Some other sources of "good copiloting knowledge": (All of the below is coming from a military perspective. May be some differences in YOUR organization.)
-The Dash 1 (I think the civilians call this the Operating Handbook or Operating manual, or some such. It's the book that tells you how to fly the plane) may specifically dole out duties to the "Pilot" or "Copilot", and it may dole out duties to the "Pilot Flying" or "Pilot Not Flying." Or it may use both sets of terms, or terms like "left seat pilot", "Pilot in Command", "Second in Command", etc. Each airplane is different, and the terminology that each uses may be different as well. Some airplanes also include a whole section on Crew duties, that deal with who does what, when.
-The regulations for your organization. Depending on who you are flying with, (regional, major, freight, military, etc.) they may have very different takes on who does what. You may find information about that here.
-Talking with the people in your organization. Talk to the other Co's (FO's, SIC's, whatever) and see what they do to help back up the pilot, but also talk to the AC's (PIC's, Pilots, left-seaters, whatever) and see if they like/dislike those things. The worst co-pilot I ever flew with was trying too hard to act like a pilot-in-command and requested changes to clearances without ever discussing them with me first. I would have traded him for an empty seat to my right any day of the week!