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Here is a quote from Bertrand Russell's The Practice and Theory of Bolshevism.
I have never met a personage so destitute of self-importance. He looks at his visitors very closely, and screws up one eye, which seems to increase alarmingly the penetrating power of the other.
I can't imagine what "screws up one's eyes" looks like. It is even more difficult to imagine "screw up one eye." I think only ostensive definition can help. Please kindly provide a picture.
Roughly, "to screw up one eye" means to tighten and tense up all the muscles surrounding that eye.
This is an image of someone screwing up their entire face. Imagine that, but more localized. And you probably wouldn't close the eye completely, but rather leave a narrow gap remaining to look disprovingly at the person with.
Basically an extreme squint.
Here is an image of someone screwing up one eye, although the child in question seems to have an eyebrow that makes the expression even more disapproving. You can kind of see how Russel's comment that it "increases the penetrating power of the other [eye]" applies.
Maybe your problem with "to screw up" is the fact that the compound element up after a verb can have so many meanings:
The temperature is going up - vertical movement upwards
He opened up the sack - merely stressing the idea of opening
He tied up the sack - meaning the contrary of opening; fastening a cord around the top of the sack and making a knot
"to screw up a bottle" means to screw the screw lid back on, to close the bottle.
