Add an Existing Google™ Account - HTC One®

If you don't already have an account, refer to Create a New Google Account.

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.
Tap Accounts & sync.
Tap the Add icon + (located in the upper-right).
Tap Google.
Enter the email address then tap Next (located in the lower-right).
Enter the password then tap Next.
Review the Terms of Service / Privacy Policy then tap Accept.
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.