Available from version 5.6.0.
This is the most preferable way to upgrade.
Command to run:
php command.php upgrade
This will check the next available version, download it and install. Once upgrade is complete it will prompt to run the command again, if a newer version is available.
To check your current version go to Administration > Upgrade page.
Go to the upgrade page https://www.espocrm.com/download/upgrades/ and based on your currect version download needed packages.
Go to Administration > Upgrade. Upload and install one by one upgrade packages.
Execute the following command from EspoCRM root directory:
php upgrade.php /path/to/upgrade/package.zip