Restoring from backup

I bought the 500GB My Passport for Mac so that I could backup my Mac Laptop at school. Every year the school district “wipes” the entire hard drives in our desktops, which is a real inconvenience to the teachers, especially to power users like myself. I backed up the hard drive to the My Passport- not stopping to think that it was backing up the system software also. Duh! So when I tried to restore all my files back to the drive in the laptop I got the message that informed me there was not enough room on my laptop to restore to.  Good grief, there went all my important documents and programs.

So I bought the 1TB My Passport for Mac, thinking that I could restore my backup in the larger drive. The drive would not let me restore the files from the original 500GB Passport drive. Just would let it happen.

I really need to recover all the date from my laptop that I backup to the My Passport.  Would appreciate any help or advice you can give. I was trying to get help from WD support, but maybe someone can redirect me…

While a power user, not very tech savvy.

What software did you use for the backup?

Assuming you used Time Machine, you can go to the drive an pull individual files if you want

the backup folder will show the computer name 

this an alternative when you can not retrieve the entire backup

not sure if you can restore to another drive then the internal drive on the Mac with TM ,  but manually you can transfer files to any place