how is Smaug finally defeated?

After Bilbo steals the Arkenstone, Smaug goes on a rampage, leaving the mountain with all intentions of destroying the lake-town (Esgaroth). Smaug attacks repeatedly, burning the town and wreaking havoc on its occupants. Unfortunately for Smaug, the thrush reaches Bard with Bilbo's news about the "chink" in Smaug's armor, something that allows him to use the very last "black arrow" to mark the spot and kill the dragon.