There are a number of tricks for getting cheaper tickets that the airline industry doesn't want you to know. Explore every option available and you'll probably find a less expensive price. For example, you can schedule an "extended layover" of a day or more, or you could even skip the second half of a connecting flight to get to your destination.
If all of this sounds too complicated, you can still save money by using Google Flights. This new tool from Google is extremely easy to use -- just enter your desired departure and arrival dates and the locations. You'll see a list of the lowest priced fares, but it will also recommend flights on nearby dates for even cheaper.