EDIT: This is part of the Dawnguard quest line, the actual mission where you can start learning Soul Tear is "Beyond Death"
*** Spoiler - click to reveal ***During the quest where you travel to the Soul Cairn, you will have to do battle with a Dragon called Durneviir. Once you have beaten him, he will greet you before you head back to Tamriel and ask a favour of you. He will gift you all 3 parts of his Summoning shout and ask for you to summon him in Tamriel.
Each time you summon Durneviir you will get give one word to the "Soul Tear" shout. So you will need to summon him 3 times. The shout takes 300 seconds to recharge, so 5 minutes; just wait an hour and summon him again ( Due to a message I need to specify waiting using the in-game "Wait" feature) . Try summon him in a wide open area so it doesn't glitch, sometimes I found him to spawn and insta-die.
You do need the third level of "Summon Durneviir" so you will need to spend at least 3 souls on unlocking all 3 levels. NOTE: You don't need to unlock any of the shouts for Soul Tear using Dragon souls. Simply having learned them is enough.
EDIT 2: Make sure you aim the shout at the ground to summon him. You will need some clear space within which to summon Durneviir. The planes outside Whiterun are ideal, although I did it out the front of Castle Volikhar