how do you determine what cable to use?

In short, measure the diameter of the conductor without the insulation - the AWG correlates with the cross-sectional-area of the conductor in the cable.

So you might imagine, once all those strands are bunched up with some space in between, a multi-strand conductor would need a slightly larger overall diameter than a solid-core conductor to get the same CSA - but not by much! Trouble is, it's hard to measure the diameter of the stranded conductor (it squishes).

Some stranded cables of the same AWG will have more or less strands - having more, thinner strands is more expensive, more flexible, slightly more compact. But having less strands is a bit cheaper. Somewhere between 7 and 32 is common for, say, 18AWG.

In general, a rough guess will be close enough. Some sizes are more common than others (e.g. 18 AWG and 22 AWG), so you can probably also compare to a known cable by sight quite reliably.

And the outer insulation varies a lot in thickness depending on material and voltage withstand rating, so the outer diameter is useless!