Depends on how old the computer is. But what Claire said. Or a docking drive if the old one isn't compatible.
The old PC is completely knackered, but I managed to rescue the hard drive, so I assume I can insert a cable to get it to appear on my new PC, I need to check what type of hard drive it is, but there will be a USB cable at the other end to plug into my new PC.
I can then hopefully copy all the files I need from the old drive.