We recommend the automatic upgrade. If you're running version 2.2+, Piwigo will tell you which plugins may be not compatible with Piwigo 1.3 before upgrade.
If you're running Piwigo 1.3.x you can also download the 1.3.x_to_1.3.1.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 1.3.x installation. No database upgrade is required.
If you are running a version older than 1.3 and do not want to use the automatic upgrade, then follow the manual upgrade.