Try Off-days and Off-hours
Yes, you want to fly out on a Friday, back on a Sunday, and depart at a nice, sleepy 1 p.m. This is perfect. And typically the most expensive way to fly.
It depends a lot on the route, but in general, the cheapest days to fly are Tuesday and Wednesday; Mondays and Saturdays can mean lower prices, too [source: Hobica]. It's sometimes a business versus pleasure thing: Airlines might charge higher fares on Mondays and Thursdays, especially for early-morning and late-night flights, for popular business-travel routes. For common vacation destinations, Fridays and Sundays at more-leisurely hours will typically be the pricier options [source: Kayak].
You don't need to guess here: Most booking sites will show you fares for several days on either end of your selected start date, and for different departure times. In a nutshell, though, if you're searching for fares to Honolulu, Tuesday and Wednesday are safe bets for starting out, and Tuesday or Wednesday at 6 a.m. might save you big.
It's pretty simple: Lower demand means lower prices. There are some discrepancies, however, that fly a bit more under the radar.