Using Office 365, booking a meeting room is no different to adding an attendee to a meeting. Simply create the meeting in Outlook or Outlook Web and add the room as an attendee to the meeting. Providing the room is free, that's all you need to do.
Outlook Desktop Mac/PC
1. Create a meeting
2. Add a location - type the name of the meeting room
3. Use the scheduling assistant to ensure that room and your other attendees are free
Using Outlook on the Web
1. Add the room as a person (not a location)