There are several airlines and websites to choose. Here are a few websites that have good deals.
Airfarewatchdog Finds affordable flights and will send you email notifications for low and unadvertised flights. Founded by George Hobica. Mr. Hobica is a travel journalist specializing in consumer issues and he's written for National Geographic Traveler and other magazines.
Kayak One search and it checks hundreds of sites for the best deals on flights, hotels, and rental cars. I've used the iPad app a few times and it gives you a good idea of price and availability.
Bing Travel Formerly Farecast.com, provides travelers predictions on when to buy your tickets. Using approximately 175 billion data points of air fares, they predict when fares will rise or fall and claim a 70-75% success rate.
Yapta This site keeps track of a flight's price after you buy it. If costs drop after you bought the ticket sometimes you can get a refund on the difference. Not everyone will do this and the refund will usually be a travel voucher or a coupon. A good website to bookmark and they'll send you an email or tweet if prices are falling.
Hawaiian Air Local Honolulu air carrier. Most prices are competitive, however since it's a small airline it might not have the best prices.
LateRooms.com I haven't used it, but heard it works like Priceline.com and works well for international bookings. Yes, this page is for air fares, but if you're late booking your flights LateRooms.com goes hand-in-hand with late hotel bookings.