on your Piwigo.com account, page [Administration > My account > Manage > tab My data], ask to retrieve your data. They will be provided as a list of 500MB zip files. You can also request for an FTP access, if you contact Piwigo.com support for that.

extract content of the zip files. In the first zip file, you will get the SQL database dump + the “local” directory. All zip files, including the first one, will include the “upload” directory.

download the latest version of Piwigo (not the netInstall), extract files, transfer them on your hosting but do not start the installation.

modify file local/config/database.inc.php so that it matches your database credentials on your new hosting server. Please note that tables have no prefix on Piwigo.com, so change

 $prefixeTable = '';

transfer directories “local” and “upload” on your new hosting server

import your database dump

you're good to go, an you may certainly have to install/activate a few plugins you were using on Piwigo.com, but your Piwigo will tell you.