(Disclaimer: I am not an expert in photo editing and I may be unaware of some conventional terminology here.)

The most obvious thing about the image, to my eye, is that it has a lot of blue and much less red. Let's look at the histogram of the colors:

(screenshot from macOS Preview)

We can see that the red channel is almost all very low, and there's a lot of dark red and bright blue (in the histogram per channel — not necessarily saying that any individual pixel has a predominantly red hue!). Let's desaturate the image so we can concentrate on the values:

It looks a lot more normal now, but it still has strong contrasts between almost black and almost white. This may be in part due to editing or film exposure processing, but it is also due to the scene: white walls, white floor, black ceiling, black escalator handrails, black carpets.

If you want to take a photo that you want to eventually look like this, look for a scene with such strongly black and white elements, and very few saturated colors. That will make the photo work better with the editing.

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To demonstrate editing, let me try to quickly mimic this effect on an arbitrary photo. Here's a picture I took of some ducks having a nice day (which is an outdoor scene, so it won't work thematically as much as the indoor artifically-lit photo you showed, but anyway):

Now, I'll apply the following “Curves” transformation in GIMP, squishing the values towards the low and high end, and reducing the red channel overall:

This is the result:

It's not as boldly cyan, because of the large amount of green grass, and not nearly as pretty, but I hope it demonstrates what kind of changes (not necessarily the exact ones I did!) can produce the effect you're looking for.

In general, you can make pictures look “old” by making their color and value reproduction worse, in ways which don't quite totally clip. This doesn't always mean pushing towards the extremes — for example, if you wanted to mimic a-copy-of-a-copy, then you might want to reduce contrast, pushing everything towards mid-tones, to mimic the effect of taking a photograph or photocopy of an existing image without exposing it perfectly.