If you want to add your Google account to your iPhone or iPad's system apps, you'll want to go to Settings > Mail or Calendar or Contacts.
Launch the Settings app from your Home screen.
Tap on Mail, Contacts, or Calendar.
Tap on Add Account.
Tap on Google.
Enter your login information for your Google account and tap Next after each step.
Tap Save in the top right corner of your screen
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.