It's very simple. A player begins the game and sends his turn to his opponent. His opponent makes his response, ends the turn, and then makes his move for the next turn. Next, he saves the game without ending the turn. At this point, he sends all relevant files to his opponent.
His opponent follows the same procedure: he makes his response, ends the turn, and then makes and saves his move.
Using this technique greatly speeds up the game. As Hobbes pointed out to me, it also enables each player to watch every other turn be resolved.
It does have one drawback: it requires that you be mindful of whether you're making your first half move, or your second half move. The method that I've personally come up with to avoid confusion is that I place an object on the left side of my keyboard, and then move it to the right side of the keyboard after I've finished my first half move to my satisfaction. I remove the object (a child's crayon

In this way, if I'm distracted by a phone call or called away from the game for some reason, I'll not be confused when I come back.
