If you "backed up" your files via an iCloud backup then just restore from the iCloud backup. If you were referring to files not associated with an iCloud backup, know that certain apps have access to iCloud and files created with those app can be restored by reinstalling the apps.
Did they send a new phone, or just wipe your old one?
Assuming your device was backed up to iCloud, you can do the following:
Go to Settings > General > Reset, then tap “Erase all content and settings.” In the Setup Assistant, proceed to “Set up your device,” tap Restore from a Backup, then sign in to iCloud. Proceed to “Choose backup,” then choose from a list of available backups in iCloud. Set up a new device from an iCloud backup.