Having issues using an HP printer wirelessly with my Mac

you can look up the user manual and and driver updates on the HP product support page

https://support.hp.com/us-en/products/printers

I have a Brother printer and it can use a direct USB connection to one computer, and that computer can share the printer to another computer over the Ethernet or WiFi network.

It also has a Ethernet port to connect to a router and share over other wired or wireless computers on the network.

Look at the printer's manual and it will tell you, likely it is either a USB cable or an Ethernet connection if you are connecting it via your router.

Depends on the printer - exactly what model is it?

And, exactly what model/specs is your Mac?