Ask the CA to "let you be the CA". You write stuff up in the mx book. You find the page in the MEL and explain it to him. You compute bingo fuel for a hold and divert. Quiet time in cruise? Ask him "what would you do now if xxx happens?" Better yet, tell him what YOU would do if it happens and have him critique it.
Ask him why he did what he did, and if you disagree with his decision, ask him to critique your thought process. Read the FOM, not USA Today. Watch the guy in the left seat and learn what and what not to do. Etc. Any CA worth his salt will be more than happy to mentor you like that.