How do you restore files from an iCloud backup

I want to restore a picture that I deleted from my camera roll on my iPhone. I have iCloud backup enabled, with the option for camera roll turned on, so therefore the picture I deleted should have a backup in iCloud.

However...how do I actually restore it? I don't see any way to browse past backups from either my iPhone or iCloud.com.

Is the backup simply used for restoring entire devices? Any way I can just pull a single file out of it?

Apple provides no interface to pull individual items from the backup. Whether through iTunes or iCloud, backups are intended to be restored as a whole, replacing the content on the device at the time of the restore.

Is it possible that the image is also in your Photo Stream? That's probably the best possible solution if you do not wish to go through the steps to restore the backup to a device (your device or another one) to retrieve the photos you are missing (and then restore things again from a more current backup if desired).

If you do need to restore the whole backup, erase the phone (Settings -> General -> Reset -> Erase All Content and Settings) then you can restore from iCloud. When restoring from iCloud, you can choose from multiple recent backups.