The  best way to book the flights are as follows:

• Set a flexible flight schedule and try to avoid flying on holidays and weekends.
• Start with Kayak.com. Check the nearby airports and check to compare with hotwire, expedia and priceline. From this search, you will find out which is the best airport to fly cheaper and which search engine gives you a better deal. Farecast also predicts that whether the price will go up or down.
• Search from  sitestep and Farechase
• Check Southwest (not share with above sites) also Jetblue, Delta, UA Airways, continental to see if they offer better deals
• Book your flights on Tuesday night or Wednesday morning when the air fare is the lowest to book.
• For the last minute booking of flight, please use site59 and hotwire.
• For how to get the best airfare of international flights How to get the best airfares for international flights