Ubuntu comes with all necessary tools to do what you want. Try to keep the server connected to the internet while booting off the live CD because live CD will let you install additional packages using apt-get if you needed any.
to check on available storage devices on your system type: fdisk -ul
this will show output like /dev/sda1 or /dev/hda1
hda1 represents the first IDE drive ... sda1 represents the first SCSI device ( i'm asuming that you have only one drive in the server so you might see hda1 , hda2, sda1, sda2 ....etc)
you will need to create a mount point then mount device listed from fdisk to mount point you just created. Something like:
mount /dev/sda1 /mnt/sda1
you can create mount points anywhere you want on the file system but it is the tradition to keep mount points within /mnt directory.
If the file system is ext2 or ext3 (which will most likely will be) then the command above will mount the drive ...
also note that the USB device you intended to attach will show up as a scsi disk from fdisk output. so if you had a scsi hard drive in the server you will see two scsi devices sda1 and sda2 .....
Ubuntu is usually pretty good in mounting USB devices by itself and it should show on the desktop as soon as you attach it so after that you'll be able to use graphical interface to copy from /mnt/sda1 to USB drive.