"[H]ow exactly does one determine exposure...when shooting entirely analog"
It is the same with film and digital. (Why would it be different? We are talking only about light, not about cameras.) Incident flash meter is the most accurate way (and also usually the quickest). Guide numbers are another, but once you start adding modifiers, the amount of accuracy decreases (unless you have previously measured the effects of these modifiers with a flash meter...in which case you wouldn't need to be using guide numbers anyhow, because you have a flash meter).
When using flash, there are always two exposures being made at the same time for each shot; one is made with flash and one with ambient light. For the flash part, aperture controls your flash exposure. Flash duration (set by the manufacturer and usually not changeable) is the closest thing to shutter speed in this equation. However, though it does determine exposure length like shutter speed, it does not affect exposure itself except in cases of reciprocity failure in short exposures. As long as flash duration is shorter than the shutter speed, shutter speed does not affect flash exposure. (If flash duration is longer than the shutter speed, exposure is affected, but this generally only happens with flashbulbs, which have a longer duration than electronic flash.) For the ambient part, both aperture and shutter control your exposure, just as they always do without flash.
It follows that if you want to show as little ambient light as possible when shooting with flash, use the top flash synch speed when shooting. With a leaf shutter this is generally '400 or '500. With focal plane shutters, it ranges from '30 to '250 on most cameras. Blocking out the mild "leakage" that can occur is very important with color film, as every light source has a different color. It is important with b/w as well, but not nearly as noticeable.