One of the coolest things Mac has come up to re-install the OS is the Online Recovery menu options. You don’t need to have a copy of the OS to do this. This works on Mac models from late 2010 and current models.
Important: To reinstall Mac OS X, you need to be connected to the Internet.
1 – Choose Apple menu > Restart, and then hold down the Command (⌘) and R keys while the computer restarts.
2 – Select “Disk Utility,” and then click Continue.
3 – Select your startup disk from the list on the left, and then click the Erase tab.
4 – From the Format pop-up menu, select Mac OS Extended (Journaled), type a name for your disk, and then click Erase.
5 – After the disk has been erased, choose Disk Utility > Quit Disk Utility.
6 – If you’re not connected to the Internet, choose a network from the Wi-Fi menu in the right corner of the menu bar (in the top-right corner of the screen).
7 – Select Reinstall Mac OS X, click Continue, and then follow the instructions.