What is a word or phrase that means you understand something from someone's look, e.g. you realize from their look that you should stop talking?
I think the word 'apparent' handles this well, unless you mean specifically "apparent from one's body language and mannerisms". In which case I can't think of a word.
I like evident (especially since it involves seeing):
easy to see or understand; readily apparent. (TFD)
It is from Latin ēvidēns, to see from.
"Perceive" is a transitive you could use.