You can back up the database files directly, but this can be dangerous if the database is in active use at the time you do the backup. There's no guarantee that you'll make a consistent and valid backup if a query starts modifying on-disk data. You may end up with broken tables.
The safest route is to use mysqldump to output a set of sql statements which can recreate the database completely (table creation + data) in one go. Should you need to restore from backup, you can simply feed this dump file back to mysql:
mysqldump -p -u username nameofdatabase > backup.sql
and restore via:
mysql -p -u username nameofdatabase < backup.sql
The .sql file is just a plaintext dump of all the queries required to rebuild the table(s) and their data.