We recommend the automatic upgrade. If you're running version 2.2+, Piwigo will tell you which plugins may be not compatible with Piwigo 2.1 before upgrade.
If you're running Piwigo 2.1.x you can also download the 2.1.x_to_2.1.5.zip archive that contains all new and modified files. Once you have extracted the files, transfer them onto your web server with a FTP client over your Piwigo 2.1.x installation. No database upgrade is required.
If you are running a version older than 2.1 and do not want to use the automatic upgrade, then follow the manual upgrade.