Decide whether or not you have an airline preference. Are you a member of a frequent flyer program and want to build up more miles for one specifically? Do you prefer airlines that do not charge for checking baggage? Is cost a major factor? This will help narrow down which airlines meet your standards and whether or not to book directly on the airlines website or to search flight on a discount search engine.
Search for flights on Hotwire (see resources), if you do not have airline preference or any time constraints on your trip. Hotwire gives deeply discounted pricing, however, you cannot see the airline carrier or flight times until after you have purchased your ticket.
Search for flights on discount travel sites such as Expedia, Orbitz and Cheaptickets for discounted flights and to easily search by cost, time and number of connections.
Search for flights on a travel search engine such as SideStep or Kayak for the most variety with the least amount of effort. These sites compare most of the discount travel websites, most airlines while also giving you the option of comparing prices with Hotwire.
Book your tickets through a local travel agent if you prefer to have a more personal experience with one point of contact.