How to Retrieve Data from Passport to install on New PC

I bought a new PC.  My ultra passport backed up my files on my old pc which was WIndows 7.  My new PC is running windows 8.  What is the correct steps to install the files from my old pc to the new one via the ultra passport.  (I did plug in passport into new pc thinking the software would automatically load on the  new pc, but it did not).  I want to make sure and do this correctly.

Other helpful info.  I erased the drive just prior to my last backup as the drive appeared to be stuck during back-up.  I did a system check and all was fine.  Then I performed a complete back-up again.  Upon completion of the full back-up, I attached passport to new pc to transfer files but nothing happened.

The key question here is:

How was the backup performed? Was it done by means of WD SmartWare? Or was the Windows Backup application used? What do you see when you open your WD Passport Ultra in Windows Explorer?