mremersaro
It depends on the system you're using, but if you're on a Linux system with MySQL or MariaDB then you can use the mysqldump command to export the database to a file, then use mysql to import it. If you're on Windows the easiest way is to use MySQL Workbench (command line options are available, but this is just easier). Connect to the old server and export the DB, then connect to the new one and import it.
Note that regardless of system, you need full access to the database you're planning on exporting.