How does being slender help Della in mastering the art in The Gift of the Magi?"There was a pier-glass between the windows of the room. Perhaps you...

The passage refers to the fact that the pier-glass mirror is a long, narrow strip of mirror placed between the windows.  This particular one must have been particularly narrow.  Della is a thin (slender) woman, so her thinness makes it easier for her to see all of herself in the mirror at once.  The apartment that Della and Jim live in is a very cheap apartment because they do not have much money, so the quality of apartment is cheap, too.   The quality of the mirror is, therefore, cheap.  Della has to observe her reflection in narrow strips at a time, so it makes sense that a thin person would be better at seeing her reflection.  That is the "art" referred to in the passage: the art of being able to see one's reflection.