Restoring to an iCloud backup has to be done in the initial setup process, which requires first erasing the phone. Also, as you seem to know already, the device you are restoring to must be running the same or higher version of iOS as the device that was backed up.
If you have any data on your phone now that is not in the backup that you want to save you'll need to do that first. Then go to Settings>General>Reset and tap Erase All Content and Settings. You will then go through the setup screens as you did when the phone was new. When given the option, choose Restore from iCloud Backup (see image below). Be sure you are connected to wifi and your charger as this will take some time to finish.