I just went throught this with a friend. First, I hope you have a backup - not because these steps will erase anything- but because it's always important to do especially before an OSX upgrade.
-Force the computer to shut down by holding the power button.
-Start up in Internet Recovery: Power on, press and hold Command +Option +R
It will load into OS X Utilieies, choose a language if asked
-Use Disk Utility to repair the hard drive: open Disk Utility and select Macintosh HD on the left side. Under the white box on the right choose Repair Disk.
The majority of the time Disk Utility doesn't find anything
but you'll know the hard drive is ok.
Once complete and if there are no issues, restart the computer normally.
-Use the Apple menu and select restart.
-Once the computer starts up it should continue the installation.
Just in case...
If Disk Utility gives an errors in red. Follow the recommended action on the screen. Worst case scenario (Not expected) : If it says "can not be repaired, back up and erase and install" this action will delete everything on the computer. Report back for advice.
