There are two ways to export a database. You can either use phpMyAdmin or SSH command. If you are not familiar with terminal commands we recommend you stick to the phpMyAdmin way.
Before exporting make sure you are on the correct database, and not information_schema. When you have clicked on the database you want to export you can easily go to the export tab and click finish. This will save the database dump locally on your computer.
When using terminal for exporting a database you have to do is access the server through shh. Once you have accessed the server you insert your information into this command:
mysqldump --single-transaction -u USERNAME -p DATABASENAME > FILENAME.sql
After filling inn your information, you are asked to enter the database password. After filling in the correct password, the server will process the information and create a database dump in your current directory.
If you want to transfer this database dump to you local machine or to another server, you can do this through the rsync command or through fileZila.