Recovering data from hdd

I have a MacBook Air (2008) and it doesn't start anymore. It seems like the hard disk drive is somehow damaged. I tried with the diagnostics and also with Disc Warrior to repair the disc, but that wasn't possible. It's the second time that I need to change the hdd of my Mac. Still, I need to copy some data from the disc.
I can start the system in console mode. Is there any way I can mount the hdd from shell and try to get some data from it?

An advanced tool like Disk Drill might be able to do it. See their user guide:
Disk Drill by CleverFiles - User Guide

There are others like Data Rescue. But bear in mind that if your drive has indeed failed, recovery may be impossible short of using a professional service that costs big $$$.

In the future, if your data is this important, we HIGHLY recommend developing a more solid backup or cloud storage plan.

How to create a bootable disk with Disk Drill?
If Disk Drill is able to mount the hdd why I cannot do it from shell?

Stick the drive in an external enclosure and try Data Rescue as previously suggested.