On your desktop, you can sync Gmail very easily. Just go to the Settings and then click 'Accounts Email App' and then click on 'Add an Account' and your Google account. Then, enter your email address and password and review the permissions, then click 'Allow' followed by a click on 'Done.' However, if the Gmail app not syncing with desktop, you need to check the sync settings in the Gmail app to make sure they're turned on. This should, of course, be enabled by default, but anything can happen. It's possible that you unintentionally turned it off. Make sure Sync Gmail is enabled under 'Data use.'
See also - gmail not syncing