*** Spoiler - click to reveal ***During the last section of the quest, Chasing Echo's - you will encounter the boss, a dragon named Durnehviir. After defeating him, make your way out of the arena and he will be waiting. He admires you for ending his undefeated streak within the Soul Cairn and will give you a Shout to summon him.
You must be in the outdoors within Skyrim (no dungeons or other-worldly dimensions), have the Shout fully upgraded (3 dragon souls needed) and an open space, like the open plains near Whiterun; in order to work. Make sure you face the ground and hold down RB until it is cast. (Although there are reports you can summon him in the Soul Cairn as soon as you get the Shout)
The summoning Shout will take at least 5 minutes to reload, however, by waiting 1 hour and casting again should easily make you achieve this in less than 5 minutes. (Thanks TuomasP)
Everytime you summon the dragon he will grant you the Soul tear shout at first, and the second and third levels afterwards.