It's unbelievably simple
You line a coffee cup (or teacup) with plastic wrap, or whatever we call it these days:
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Then you pull the corners of the plastic together and scrunch them up:
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Then, you just dump them into some simmering water. This picture is only for two eggs, but if you use a slightly larger pan, you can get a dozen in there, no problem. Just rub a little bit of oil on the plastic before you add the egg; it makes it easier to remove it.
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I learned this from a restaurant I once went to. No fancy egg poaching thingies (which will only do 4 at a time) and you only need 1 cup to make 4,6,8,10,12 eggs.