From a Home screen, navigate: Settings > Accounts.
Swipe left or right to access apps; steps apply to the default Home mode.
Tap ADD ACCOUNT.
Enter the Gmail address then tap Next (located in the lower-right).
Enter the Password then tap Next.
If presented, tap Back up data to your device's apps, app data, settings and Wi-Fi passwords to enable then tap Next.
Enabled when a check mark is present.
If presented with "Set up payment info", tap Remind me later then tap Next.
To set up payment info after adding a Google account: