The OS X upgrade couldn't be started because the disk is damaged and can't be repaired

Apple has two simple articles listing the exact steps needed to fully erase your startup disk and get a clean OS installed from the Mac App Store:

• https://support.apple.com/kb/PH21973
• https://support.apple.com/en-us/HT204904

The first (PH21973) is shorter and to the point and the second has many helpful pictures, explanations and links to other resources. You should expect about 10 minutes to print out and read through the instructions, 10 minutes to do the wipe and an hour or so to download and reinstall the OS. If you have a very slow internet connection or Apple's servers are slammed due to it being the day of a major iOS or OS release, you might need 4 hours or more to complete the OS X download.

Also - some apps like iLife and iWork are not included in OS X even though they came with your Mac initially. Be sure you back them up or verify they show up as purchased apps if you don't want to have to buy them again. AppleCare can help if you can't find your purchases or need a backup.