Nowadays it’s easy, load up your fancy editing software, select the thing you want to edit in, change its alpha value (even the method for alpha mixing is pretty simple were you to have to do it from scratch with only a graphics library for some strange reason).
But how did they do it when they used… what do they call it? Starts with an “f”… film! That thing! Editing in something opaque seems easy enough, super-impose two things, with the thing you want on top closer to the light, and shine a light through to another piece of film. Bingo, the new cell on the new reel of film has the original image with the opaque part on top (or maybe I’m off on this too).
But how did they do transparency, cross fades, etc? My guess is that it involves reflection or lenses in some way, but that’s really a WAG based on what little I know about how to manipulate light.