Here's a test to perform - using a computer's browser, log into icloud.com and go to the Contacts page. If they are gone, then they are gone (must have been a setting during the update to iOS6).
If they show up, then the problem is that your device is not connecting to the Contacts database on icloud.
On the device, go to Settings>icloud. Be sure icloud is on and using the right ID. If not, scroll to the bottom of the page and tap Delete Account - this just disconnects the device from that account, no data is lost. Then log back in using the correct ID. ALSO - be sure the Contacts are turned on (on the same screen).
Note: Contacts are not part of an iCloud backup, since they are part of contacts database on iCloud's servers. So performing a restore will not help.
Contacts are gone from icloud.com.
Then they have been deleted. There are many reasons for this. One possibility is that someone else is using the same iCloud account (family member, etc.) and they deleted contacts, thinking they did want them on THEIR device. How to get them back? Unfortunately, an iCloud backup does not include any of the sync databases, like contacts, notes, calendars, reminders, etc. because the data is already stored in these databases. Your only hope for restoring the data is if you had that data on a computer (like a mac's Contacts, Calendars, etc.) and that data was backed up using whatever backup software you typically use (e.g. Time Machine on a mac). Just restore the data files back to the computer. Other than that, I'm afraid the data is gone.