How are the best director award winners chosen?

From eHow:

In Hollywood, the nominating and selecting for the Oscars are done by the writers, actors, directors, animators, art directors and executives. The only requirement is that each participant be a part of the Academy of Motion Picture Arts and Sciences.

Members of AMPAS are courted by film studios with free screeners, gifts and social evenings in the run up for most award ceremonies. Considering how much extra revenue is on the line when a film wins an award, the expense of these promotions are considered well worth it.

When I was a member of the Animator's Guild, I would be sent screeners of the major films released that year, along with cells from the films, making of books, postcards, whatever would work to secure my vote.

Then the nomination ballots are mailed to all AMPAS members, usually in December, and they have a limited amount of time to get their votes in.

In the case of the directors' awards, your statement 'It seems impossible to assess the method of a movie director unless you are part of the crew' is correct, but the directors are being assessed on their output, not their method. Subject matter can be a great influence, as can the current zeitgeist or even a really solid marketing campaign. It's a general rule of thumb that films picking up awards early in the season jump on the rollercoaster and pick up speed all the way to the Oscars.