If you don't already have an account, refer to Create a New Google Account.
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From a Home screen, navigate: Apps
> Settings.
If unavailable, tap the Apps dropdown menu
(located in the upper-left) then tap Alphabetical. If still unavailable, refer to Manage App Icons.
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Tap Accounts & sync.
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Tap the Add icon + (located in the upper-right).
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Tap Google.
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Enter the email address then tap Next (located in the lower-right).
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Enter the password then tap Next.
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Review the Terms of Service / Privacy Policy then tap Accept.
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From the Google services screen, tap Keep me up to date... to enable or disable then tap Next.
Enabled when a check mark is present.
Related Topic: Remove Gmail™ Account