Which project management processes am I most likely to run into as I manage a construction project? What should I be aware of as I try to learn more about the specific intricacies that affect project management, in the construction field?
Your first construction project is going to be a bear. Hopefully, you've been around construction a bit gaining familiarity with the process. I believe one of the best things a new CM can do is spend time trying to anticipate upcoming problems, rather than spending all your time reacting to them. Be familiar with what is coming up on the schedule, and what your crew will need to complete the task. Where are their holes in the construction documents? Where will the code enforcement official stick a wrench in the works? What conflicts are likely to arise between your sub-contractors as they work in the same area?
The best case studies will be your own
I am an architect, and the first big construction project I "administered" (not managed) taught me invaluable lessons that have made every subsequent project easier. While I can't point you to a direct answer or resource, I recommend noting or journaling about your experiences as they happen. Those notes will aid you the next time around.