You can use this Google Flights to find lower fares and book your airline flights online. When you begin, you will see several search options, including the following:
If you perform a search, you will receive the best departing flights (and the best return flights, if you selected round trip). But look a little closer and you will see even more helpful options.
For example, Google Flights might inform you that if you flew a few days earlier or later, you could save even more.