Basically, I have a Yamaha EG 112 that needs a new nut to work. How would I go about finding out if the nut I'm ordering would fit it?
...is there something I'm missing that makes this a stupid question?
Measure it. You'll need to know the length, width, and height. If you're buying it preslotted you might want to see what radius and string gauge it's made for. They're almost never a direct drop in so if it's a little long you'll need to file it and if it's a little short you'll need to shim it.
Measure the current nut, length, width and height. Measure the string spacing. Check for whether the slot is curved or flat bottomed. Order the appropriate nut to match those sizes. If none are available, be prepared to slot a blank yourself or take it to a luthier or tech to have one made for you.