Question: how to calculate confidence interval step by step?
Answer: α : subtract the given CI from 1. 1-.9=.10.
z α/2: divide α by 2, then look up that area in the z-table. Not sure how to read a z table? ... 
: Divide the proportion given (i.e. the smaller number)by the sample size. 57/510=0.112.
: Subtract. from 1.