(Edited to replace previous text, I seem to have fixed my original problem).
I’d been trying to get my PS3 controller to function in Retroarch unsuccessfully but I finally stumbled upon a tutorial that explained the rather small and easily missed step (turning on the PS3 controller only AFTER Retroarch is told to use it) that got things working for me.
Since I got my question answered, and since I can’t delete this thread, I figure that I might as well use the opportunity to ask an entirely different question: How do I map the controls? I see a couple of different spots where I can do such a thing but when I tried it (in the Retroarch space invader menu, while a NES game was going) all I managed to do was completely deactivate the controller causing a complete restart of the program.