You can do this only by exporting your tables from the database directly, the plugin does not have a settings export feature.
There are three tables: wp_participants_database keeps the records, wp_participants_database_fields keeps the field definitions, and wp_participants_database_groups keeps the groups definitions. To transfer the entire contents of the plugin, you’d export all three.
Finally, the main settings are in the options table, in an entry named ‘participants-database_options’ contains the settings (everything under the “settings” menu) for the plugin.
After installing and activating Participants Database on the new site, you’d replace the default data the plugin installed with your exported/copied data from the first setup.
