It's one of the more confusing aspects of English. Generally, the answer is in the form of the following equation:
x y z = z's x
where x is the object, y is the possessive word or phrase, and z is who or what x belongs to. For an example in English to English:
pants of Paul = Paul's pants
car of Ali = Ali's car
From Spanish to English:
pantalones de Paul = Paul's pants
el auto de Ali = Ali's car
All four mean the same thing, but the right side is what's considered grammatically correct. To further complicate things, you can use possessive phrases to make the left side not only sound grammatically correct, but also give more precise meaning. For example,
Car belonging to Ali = Ali's car
means the same thing, but
Car which belonged to Alie =/= Ali's car
In some instances, you could use the form "x of y" to convey a different connotation/feeling. In your example, "the beauty of a woman" has a different connotation than "woman's beauty"; the first has a more poetic tone to it and the latter, a more casual tone. It depends on the context.
Check this link out for more examples.