Several ways.
If the drive is actually ok but just unreadable for whatever reason, you can put it in the machine as a secondary and copy files that way. If it's SATA, no problem, just hook it up to the SATA port and power it. If it's IDE, then make sure you jumper it correctly for master/slave. Also, if it's SATAII and you motherboard is plain SATA, then jumper it for plain SATA first.
If it is readable but the partition is lost, then use something like partition recovery or file recovery software. These guys work good, I've used them in the past and it's pretty cheap:
Active@ Partition Recovery. Recover Deleted Partition. Undelete NTFS & FAT partitions.
If it is unreadable as a drive and the USB case is fine, then you'll need to send it off to a company like
gillware LLC to retrieve the files. Prices last I checked were from ~350 to 800 dollars. WD might do it, but I bet it will be more expensive.
If none of this makes sense to you and you aren't good with opening up and working inside a computer or USB case, then take it to a tech.