|"I have no idea how to do that"|
Which bit, producing a Puppy Live Linux CD or connecting the external as an internal drive? Just for starters:
With Puppy you burn a CD then boot up to Linux with it - it just temporarily runs from the CD drive and the RAM. You can then look at your external drive in Linux and see if it can be read. If so you could save the contents elsewhere.
If your external HD is in an enclosure (caddy) then it can be physically removed and put inside your computer. If it is a premade unit then you cannot do this.
Always pop back and let us know the outcome - thanks