Mac start up - Flashing Folder
Try OS X Recovery, which is supported in Lion and later and hopefully on your Mac (if your Mac shipped with Lion it is supported, otherwise see http://support.apple.com/kb/HT4904 for a list of older Macs that support Lion Internet Recovery. If your Mac is not listed you will need the OS X Recovery Disk Assistant, see http://support.apple.com/kb/DL1433).

To start up into OS X Recovery you need to turn on your Mac while holding down ⌘R (http://support.apple.com/kb/HT4718):


  OS X Lion or OS X Mountain Lion includes a built in set of utilities
  in the Recovery System. Restart your Mac and hold down the Command key
  and the R key (Command-R), and keep holding them until the Apple icon
  appears, indicating that your Mac is starting up. After the Recovery
  System is finished starting up, you should see a desktop with a OS X
  menu bar and a "Mac OS X Utilities" application window. Note: If you
  see a login window or your own desktop and icons, it is possible that
  you didn't hold Command-R early enough. Restart and try again.
  
  In order to reinstall OS X Lion or OS X Mountain Lion, you will need
  to be connected to an Ethernet or Wi-Fi network. The Wi-Fi menu item
  is in the upper-right corner of the screen. Click the icon to display
  all available Wi-Fi networks. Click your preferred network name and,
  if needed, enter a username and/or password.


(You will be given the chance to restore from a Time Machine backup, which works very nicely and I'd highly recommend.)

Read the rest of the article for more information on how to proceed.