If you have a backup of, say, an MS Word document, you open that with MS Word. If that isn't installed on your new computer try OpenOffice Writer.
And the same goes for all files in your backup: you open them with the same program as was installed on your old computer, or a compatible one.
Maybe something is missing in your post?
My old computer went on the blitz.
I backed up my files with a Passport Elite.
How do I open them, now that they are on the new computer?