There are many ways to backup a MySql database such as:
- WordPress plugin database export
- PhpMyAdmin (Most common for shared hosting)
- Heidi SQL
- MySqlDump (Most versatile)
- WP-CLI database export (Recommended for WordPress)
From all of these methods my personal favorite method is to use WP-CLI, however this method may not be available to you if you are using a shared hosting provider and you need to be comfortable with some command line, in this case the most common method is to use PhpMyAdmin or use a WordPress plugin.