For most travelers, the easiest and most intuitive way to compare flights is through one of the many fare compare websites. Examples of these websites are Kayak.com, CheapFlights.com and CheapOAir.com. Just type in your travel dates and destination, these websites do all the searching for you.
Most of the fare compare websites will link you to consolidator websites such as Expedia or Orbitz. While this will save you time from going individually into each of those sites, the prices will not be any different.
Also be aware that some websites will charge a fee for booking the ticket, which is on top of the published airfare. Try to choose a website that does not charge fees for booking.
Sometimes airlines will only publish the best rates on their website. It cannot hurt to double-check your rate against the actual airlines website to ensure you have found the best deal. This extra little step could possibly save you a significant amount of money.
Before the advent of the Internet, the only way to book a flight was through a travel agent. The travel agent would have a large book full of the published fares for that particular time period, usually a week or two. Once you and your travel agent chose a flight, the travel agent would have to call the airline to book the flight.