I think this is a valid question if it isn't a simple FAT or NTFS volume the user is trying to recover data from.
For example, the WD MyBook World Edition NAS uses ext3 OS partitions with an XFS data partition so unfortunately you can't just take the drive out, put it into a caddy and view on a Windows PC (although you will need a SATA drive caddy or adapter).
If you haven't got Ubuntu installed, download the ISO and run it from a Live CD/DVD. Don't connect the caddy/adapter yet.
First create a mount point directory in which the contents of the file system on the device will be displayed by loading up a terminal and typing:
Then type the following command:
This will give you a list of hard disks and partitions currently visible to the system, e.g.
sda sda1 sda2 sdb sdb1 sdb2...
Hard disks are the entries like 'sda' and 'sdb', and their partitions are the numbers which follow that entry, like 'sda1', 'sdb2', etc.
If you now connect the drive and run the command again (press 'Up' key followed by Enter) you will see some new entries in the list. When examining my MyBook World Edition the device was sdb and the XFS partition sdb4. You can also use tools like gparted to display the partition table and therefore show you which partition is the largest and clearly the data partition on the drive.
Once you have identified the partition run the following command (if your partition is /dev/sdb4):
sudo mount /dev/sdb4 /media/wd -t xfs
As long as there are no errors, you should now be able to browse the contents of the drive by typing the following commands:
Which will provide you with a directory listing. If this looks like your drive, you should now be able to access it through the file manager in Ubuntu.
In regard to copying the data off, you have two routes. You can either make a logical copy using the copy 'cp' command, which means you can copy the contents of your drive to a drive which will be accessible to your main computer (i.e. NTFS for Windows or HFS+ for Mac), or you can perform a physical device image as per the other answer (which suggests utility dd-rescue) which will preserve all content in unallocated space but will still be in XFS.