1. Launch the Settings app from your Home screen.
  2. Tap Mail, Contacts, Calendars.
  3. Tap Add Account.

  4. Tap Gmail.
  5. Google's authenticator screen will pop open, where you can enter your email address and password. You also may be prompted for your two-factor authentication code, if you're using one. (And you should be. Here's how to set one up.)
  6. Tap Allow when prompted with the "iOS would like to..." screen.

  7. Choose which services you'd like to sync: Mail, Contacts, Calendars, or Notes. You probably want most (if not all) of them on.
  8. Tap Save.

After you save your account, you can access your settings at any time by tapping the Gmail entry under the Accounts header. If you'd like to change the description from "Gmail" to something more apt, tap the Account button, then tap the Description field.