There are two plug outlets. There is also a switch, part of the same unit, which turns a built-in light on and off.
Through numerous trips back and forth to the fuse panel I have discovered that the light switch is controlled by a different fuse than the two plugs - one of which as I mentioned recently stopped working.
I friggin hate electricity - I can't understand it. Plumbing isn't quite so bad. I'm really good at sawing a 2 X 4 in two pieces.
So you have a switch on a completely different circuit from a two plug receptacle occupying the the same box under the same plate, if I've interpreted your description correctly. Given that you say you hate electricity and can't understand it, the safest thing would be to mark the fuse that supplies the switch and its light, plug something like a radio into the working plug and determine which fuse supplies it, so you can mark it, then call an electrician.
Besides having him fix the plug, you should talk to him about getting the switch into its own box, or ganging the breakers (harder to do if they really are fuses); it's dangerous to have a live and a deactivated circuit sharing a box. But don't yourself frustrate yourself with stuff that makes you nuts. Not dangerous stuff, anyway.
The only thing it makes sense for an amateur like you or I to attempt,
after removing both fuse/tripping both breakers and demonstrating there are no live wires in that box would be to replace the problem receptacle with a brand new one, wire by wire in
exactly the same positions (hopefully black to brass, white to silver, but amateurs don't know enough to 'correct' what formerly worked). If the problem's in the unit itself, that'll fix it, if the problem persists, you haven't made it worse, but you will need that electrician. Besides, someone who didn't know what you now do about two circuits in that box could electrocute themselves, so the electrician should get a call anyway.