[dnanian]

Before you have it looked at, please test your backup to make sure it's what you expect (it should be a "Backup - all files" made with "Smart Update" or "Erase, then copy", written directly to a properly partitioned & formatted drive as explained in the Frequently Asked Questions in the Help menu).

If they replace the drive, it'll likely come with an OS already on it. When you first start up from that drive, it'll ask you if you want to 'copy from another Mac'. Point that at the backup volume and it'll bring in your applications and data.

Otherwise, you can hold down Option during power on and select the backup drive. Once started up from that, run SuperDuper!, select the backup drive as the source, the new drive as the destination (assuming it's properly partitioned & formatted, as it should be), "Restore - all files" and "Smart Update". Run that, then start back up from the internal and you should be all set.