Hello!
Managing the preferences for your Calendar are handled within the Settings rather than directly within the Calendar app. To manage the accounts that are synced to Calendar, go to Settings > Calendar > Accounts. From there, you will see a list of all currently associated accounts, and an option that reads "Add Account". Tap on "Add Account" and you will see a list of available providers including iCloud, Exchange, Google, Yahoo!, Outlook and Other.
You may apply the same process to link accounts to your contacts. Simply go to Settings > Contacts > Accounts. You will see the same list of Internet accounts when you tap on "Add Account".
All of the aforementioned steps may be applied to Notes as well as Reminders.
Best of luck to you!