I hope this is a very stupid and basic question!

Download this, HP Printer Drivers v5.1 for OS X once downloaded double-click to install. Restart your Mac, and make sure printer is on. Open System Preferences> Printers & Scanners, is your printer listed. If it is not click on the plus button and see if your printer is now shown.

NissenHuts wrote:

First off.....I'm 68 and fairly green re technology,

I have an HP Photosmart C3100 printer ( very old I know!) and a Mac mini (10.13.6 High Sierra).

How do I make them cooperate please?

According to Apple's list of supported printers, the HP C3100 is in the list. That is, the OS should offer to install drivers for that model without having to go to HP's site to obtain them.

If you haven't yet, follow Eau Rouge's link to the HP 5.1 drivers.

HP are notorious for not supporting older printers. You may be able to use it by using a Gutenprint driver - I had this same thing with a Deskjet 990cxi and got it to work with Gutenprint, but it doesn't handle colours well and there is no duplex printing. All you can do is try. Start here:

https://sourceforge.net/projects/gimp-print/files/gutenprint-5.2/5.2.14/