Generally try and book your tickets 21 days out for the best price, and then certainly 15 days out.
Why? That's when the computer systems of most airlines get rid of the reserved but unbooked lower fare reservations.
You can hedge your bets further by scheduling flights during dips in demand such as mid-day (generally 10 am to 2 pm) or mid-week (Tuesday, Wednesday or early Thursday). And Increasingly, the price gap between one-stop and non-stop flights is widening, so always be sure to check both options.