It's all about organization. On set someone takes notes as to which take was good, and every shot is slated (the clapper board at the beginning, som calling "scene 3B take 4").
Even then, it's not all about the "good take" on set. A good editor many times will pull from a lot of takes to build the scene, even if take 4 was best for 3B, he will mix a bit of take 2 and 5... or whatever.
As far as what the director wants, it's the director's job to either communicate that, or more common in the film world, sit with the editor and you talk over choices together while you edit.
Hope that helps!