I have frequently seen figures painted as black and white objects, like as if it was a seen from an old movie or so. I have become rather fascinated by this way of painting.
However I have absolutely no idea what kind of paint to use. Is there a paint set with different shades of gray? Is there a tutorial somewhere to read? Please fill me in?

Yes, i also found some photos here. I thought, it was a campaign or a topic. I´m not sure.
Perhaps you can search for some images or topics and I also will do this and if I find something, I can add it here.
I also was fascinated by this photos!
Perhaps some of the "makers" can help you.

greetings...
Soeren

edit:
I found the topic "Monochromatica"!
https://armorama.kitmaker.net/forums/141064&page=1

It's not really any sort of mystic art Really just painting in shades of grey, black and white. A trick is to convert a colour picture of the figure you're painting to greyscale, and using that as a reference lay your palette.

If you're looking for paint sets, Andrea Miniatures produce a variety of colour paint sets - the problem though is that you can't buy the pots individually so you end up having to buy an entire new set for 1 or 2 colours