Yes, that is the right way. It is not super short and simple, though. Once you have put a fresh Install of Windows on your HDD, it has NO info in its fresh Registry of any of your application software. So you can NOT simply copy your old software files from the backup to the HDD. You actually have to re-Install all of your application software so that process can place the correct info into the Registry for each app. THEN you can copy the user-generated files from your backup to your HDD.
BEFORE going any further, you might look on the Microsoft website or around the web for some utility that can do much of this for you, possibly by copying info from the old Registry to the new one. It will be labelled for assistance in re-installing Windows, or something like that. I dont know whether such exist, or how well they work, but I'd certainly look first.