I am using DELL-INSPIRON 15R with a dual boot of Windows 8 and Linux Mint Olivia 15. It has been working properly since it was installed. Now, it is showing the error that "no file system found. grub rescue->" What should I do for this?
There is no general way to solve this issue. All you know at this point is that your computer isn't bootable.
If you've changed your BIOS settings, restore them to a known good state. If you've changed your disk configuration, restore it to a known good state.
To investigate what's going on, boot your system from a live CD or live USB. SystemRescueCd is good for this. Once it's booted, you can check if your RAM is ok, check if your disk is ok, explore your partitions, etc.
This happened to me once when the BIOS (for some unscrutable reason) decided to switch the order of the disks in my machine (two SATA disks). Other reasons could be a broken disk, a filesystem over which something scribbled, ... Check the grub command manual. Yes, that one should be online when you are flailing with a non-booting system...