There are two ways of doing it:
- Install Google Play Games App.
- A new username is automatically created.
- You can use this for Google Achievements and Leaderboard.
(OR)
- If you have already installed Google Play, you will be asked to authenticate the ID that you wish to use for the game.
- Once you select this, the account is automatically synced with the game and you can use it for accessing Leaderboard Achievements.