Go into the account settings in your phone's menu. Select the Google account you want to remove. Then while viewing that, press the menu key (if you have one) or the 3-dot icon (should be top-right corner, but different manufacturers are not consistent) and there should be an option to remove the account.
The menu layout may vary a bit between devices and android versions, so this may not be exactly the same on your phone, but there should be something close to this.