Forget code for now, you need a design, and for that you need data structures that support the desired functions. Think about these questions, get some paper and start drawing:

• How do you store each user's calendar? What data items are needed?
• What actions must be taken on a calendar to add or remove an appointment?
• How will you whether appointments on different users' calendars represent the same meeting or not?

Once you figure out that, the rest is just code to implement data changes (add to, delete from, check calendars), or carry out actions when data has been changed (like sending e-mails).