If it is an already formatted drive and it is working, your system should automatically recognize it.
WHen an external drive fails, the problem is either the USB (or other) interface or the drive. The only way to reliably test is to install the bare drive in a PC.
If the BIOS can see the drive but the OS cannot, the drive mechanism has failed, you are pretty much out of luck without resorting to "big bucks" data recovery.
If the BIOS cannot see the drive, you have a small chance. It is possible that the drive electronics died, but the drive mechanism is still OK. In that case, you may be able to recover your data by replacing the printed circuit board from an identical (including version) drive.