"Lindisfarne, The first question should be is when you insert the thumb drive into the mac, does an icon appear on the desktop?"
Before you can double click a song or drag the music files to your iTunes folder, the drive has to be mounted on your desktop.
If you don't see the thumb drive mounted on the desktop as a volume, then do as Zd542 suggested and restart the computer with the thumb drive in the USB slot. This will always work unless there is something wrong with the drive itself or the way it's been formatted. It's possible the drive has been formatted in FAT32, but even though Macs prefer "Mac Journeled", it should still see the thumb drive.
If you still don't see the drive on your desktop after a restart, then launch Disk Utility in your Utilities folder which is nested in your Applications folder. A easy way to access this app from the finder is to type COMMAND+SHIFT+U. Tis will open the Utilities folder and then you launch the Disk Utility app.
When you launch Disk Utility you'll see a list of drives and volumes on the left side. You should see the thumb drive listed there and be able to select it. DO NOT reformat the drive. Click "Verify", "Repair". Hopefully this will get it to mount.
After all that I will note one thing. I have seen friends over the years say, "the drive won't mount!" When all along it was sitting on the desktop. They either didn't recognize the name of the drive or couldn't see it because there were a jillion other icons confusing them.