It took me 2 hours of searching online and walking around shouting at the ground.
Here is how to summon him. Its simple and you will be slapping your forehead(I know I did).
The shout he gives you in the Soul Cairn is "Summon Durnheviir" (obviously).
This shout (unlike all the others) takes three dragon souls to unlock it completely.
Very important: it is a three part shout!
I am over emphasizing this because it seems to be the one thing the other forums I read do not explain. I only had 1 unlocked so it wasn't greyed out in my list of shouts and appeared to be usable. Not the case!
Again: It will not work until you spend 3 dragon souls to unlock all three words of the Summon Durnheviir shout.
Once that is done, go to a open area, relatively flat and shout at the ground in front of you.
You don't need to be in combat nor do you have to be on completely flat ground. Just a open space with no trees. (Mammoth camps or farms is a good place.)
The area outside of Whiterun is where I did mine.
Shout at the ground in front of you and when he appears, he will give you one word of the soul tear shout. He will then fly off and circle you for 5 minutes. (You can use the wait function to speed this process up).
Shout again and he will give you another word. Same process except you have to wait a couple hours. Use the wait function again. Shout a final time and you're good to go.
Hope this helps.