To do a manual backup a mysql database, use mysqldump with the following syntax:
mysqldump -h hostname -u user -pPassword dbname >/path/to/file
Note that hostname is optional and will default to localhost. Depending on some settings user and password may be optional as well.
Now, asssuming you are using a linux shell, if we want to have rotating logs, add the date name and stick the whole line in a script running in cron:
mysqldump -h hostname -u root mydb > /path/to/backup/$(date +%a)