boot into single user mode (<apple> + s)
run /sbin/fsck -fy
run /sbin/mount -uw /
make a directory in /Volumes (mkdir /Volumes/DirName)
mount usb drive /sbin/mount_msdos /dev/disk1s1 /Volumes/DirName (disk1s1 is my external drive and the specific partition I want to mount
use rsync to backup files (rsync -av /folder/to/copy /Volumes/DirName (will make a “copy” folder in the DirName directory)
make sure to unmount your external drive, and then remove the DirName directory (it should be empty after unmounting) - use rmdir /Volumes/DirName (it will complain if the directory is not empty)