Most controllers let you know physically by emitting a beeping sound and/or lit up warnings lights on the drive tray of the broken disk.
Also, any RAID controller can be monitored using software tools. Most RAID controllers are manageable using software tools, so you can eg. configure new arrays, set spare drives, replace disks, migrate RAID level, etc, etc. Those tools can also be used to verify the health of the array.
These tools are often incorporated in some kind of script that shows the RAID health in a single line, so that the output of the script can be incorporated into some kind of central monitoring system such as Nagios. But ofcourse, you can also simply periodically check it manually or run some sort of cronjob.
Also, some RAID card manufacturers supply software that allows it to send an e-mail in case of problems. eg. the 3Ware cards can be used with a tool called
3dmd, which is a daemon and can sent you can e-mail in case of problems. But not all manufacturers have these kind of daemons available.
I recommended you simply google on your RAID card model and add 'monitoring' to the search query, that should yield enough results to get u going.
In a comment you stated that you are using a 3Ware card. Then I recommend downloading
3dmd, which does exactly what you want.