Usage patterns
〈事〉を手帳に書くto write something down in one's notebook/planner
I wrote the meeting schedule in my planner.
手帳を見せるto show one's certificate/ID (e.g. police, disability)
The police officer showed his ID and questioned the man.
手帳をつけるto keep a notebook/log of daily notes
I make a point of keeping a daily planner.
手帳を確認するto check one's planner (for a schedule)
I checked my planner to make sure I hadn't forgotten any plans.