Hi!
It would be the best to make 2 separate backups:
1. Files backup
2. Database backup
To make files backup you can simply create a .zip or .tar.gz archive of whole store directory. If you have PuTTY you can run:
zip -r magento_backup.zip public_html/
replace public_html/ with your actual store folder name.
To make database backup run this command from PuTTY:
mysqldump -udbuser -p --routines magento_db > magento_backup.sql
replace dbuser with your actual mysql user and magento_db with your actual database name.