From a Home screen, navigate: Apps icon > Settings > Accounts.
Tap Add account.
Enter the Gmail address then tap Next (located in the lower-right).
Enter the Password then tap Next.
If preferred, enable the following then tap Next:
Enabled when a check mark is present.
Back up data to your device's apps, app data, settings and Wi-Fi passwords
Keep me up to date with news and offers from Google Play
If presented 'Set up payment info', tap Remind me later then tap Next.
To set up payment info after adding a Google account: