In free edition of the Microsoft SQL Server - Express - you have no possibility to schedule backups. But you can set up backups with the help of Powershell scripts and Windows Task Scheduler.
Take a look at the script - that's my way to SQL backups. The script does not delete old backups, but please read my article Deleting old files and folders in Powershell, it will help. And also - Running Powershell script in scheduled task.
Please notice highlighted lines - there you will have to set your SQL-instance and path to backups.