External HD problem

I got a new macbook cus my old one was too damaged to repair, and they sent with it the old HD in an external case.
I plugged it in (Plug & Play) and Time Machine can recognize it, but theres no way for me to get into the stuff on it so I can recover my files.
I need some help fast, as there are VERY important stuff on it!

How do I get to the stuff inside the external HD?

When you connect it to your Macbook, does it appear on the desktop?

Go to: "Finder / Finder Preferences / General" and make sure the boxes are checked for "Show these items on the Desktop" then restart.