if you turned on iCloud when you activated your phone, you are already backing up you contacts, calendar to iCloud. iCloud backs up whenever your phone is on, plugged in to charge, and asleep ( not off )
IF you look in settings under iCloud it will show if backup is on and when it did the last backup.
logon to icloud.com on a computer to see your contacts list, pages, calendar and "find my iPhone"
Settings > iCloud > toggle on Calendar to ensure your calendar is backed up. To add calendars go to Settings > Mail, Contacts, Calendars > Add Account > select account > make sure calendar is toggled on.
Hope this helps..