Well it depends. Sometimes if you don't really care where you go is you can go and see if there are any open seats on a flight about to leave. When the plane is about to leave, any unsold seats are lost money to the airlines, so they can sell them for cheap. The problem is you have to stay at the airport with your bags ready to go. You can't plan it, or where you go.

Otherwise just Google, or use the travel search sites like travelocity.com or cheapflights.com etc.

I don't know but i really wonder this too - sane question

It really depends on your timing really.  Flights can be cheaper on certain days, seasons, or even something last minute like Steve MP mentions. But like he said, you have to be already at the aeroport to obtain the flight.  I've used Best Travel Store in the past but there's also Kayak, Travelocity, Hipmunk, Vayama, Sky Scanner,  Hotwire,  Flight Fox and many more. Compare flights and see what you get. 

General rule: Booking flights in well advance usually gets you the cheaper the flight.