Open your home directory by clicking on it. You should see your drive listed. Double click on it and it should open. Then right click on the file and choose "copy". Then in the open drive right click and choose "paste". Or just drag the file into the drive.
If that doesn't work, you will have to mount the drive in root using terminal (Applications > System > Terminal) :
sudo mount /dev/sdb1 /mnt
Then copy file and send it to the drive:
cp /path/to/file /mnt
Hope this helps.