Google Flights is the easiest, most flexible way to search for cheap fares, especially if your travel plans are flexible. I often make impromptu travel plans and Google Flights makes it easy to explore the possibilities. I just pick a date range, my home city - Austin, TX - and a maximum ticket price and Google Flights creates a map view with all the viable destinations. I haven't found any other flight search tool that allows for that type of search. It's so convenient.

Below is an example of the search results for all flights from Austin that are under $400 for June 3 -7. If you click on a particular city, you'll see the flight information. It's great!