Re: seriously new to this
Okay, let's bring things back to basics.
When you boot from the USB drive, Ubuntu is just running in your computer's RAM. If you try to save any files to the Home directory, that's ONLY present in RAM and will be lost when you turn the computer off or reboot it. So you don't want to save your recovered files into the home directory.
What you need to do is boot from the USB and then plug in a USB flash drive or USB hard disk to save the recovered files to. Or, insert a blank CD/DVD and double-click it when it appears on the desktop, and drag your recovered files to it and burn the CD.
You can actually run Ubuntu from a CD and then use your blank USB to store the recovered files from the damaged USB, if you don't have three USB drives and three spare USB ports
Your damaged USB drive, assuming it is readable, will appear in the sidebar on the left of the screen. Click it once to open it, you can then drag the files from it to the blank USB or to a blank CD (and click the Burn button!) to recover them.
HOWEVER: If the damaged USB drive became unreadable as the result of physical damage, it's highly unlikely that anything will be able to read it. If the drive became unreadable due to data corruption then I'd say there would be a chance, but for physical damage you'd be very lucky if any operating system can read the contents of the drive.
I try to treat the cause, not the symptom. I avoid the terminal in instructions, unless it's easier or necessary. My instructions will work within the Ubuntu system, instead of breaking or subverting it. Those are the three guarantees to the helpee.