Both servers have phpMyAdmin installed. The database size is under 50MB. The database export file is small enough to overcome upload size limits (note: you can compress the file before uploading ...

A running instance of phpMyAdmin A user with full access to the databases (such as the phpmyadmin user) A database to back up With those things at the ready, let’s back up and restore that data.

As WordPress notes, "A good hosting package will have this included." If you have backed up your WordPress database, visit your hosting service and log in to its phpMyAdmin program.