When you arrive in the Soul Cairn, you'll have to travel quite a ways. Your destination is out amidst the two glowing towards in the distance. You'll have to go through a large wall that separates the outer part of the Soul Cairn from the inner part. Go through and then make your way along the path. You'll come up to a large structure with a purple shield. When you get there, you'll have to wait for Serana to come up before her mother will appear. She will come up and talk to Serana through the shield, then you.
After talking to Valerica about the prophecy, she will send you out to bring down this shield. There are three large towers (these are the ones that are actually glowing). You will have to travel to each of these in turn and defeat the Keeper of the towers to get rid of the shield.
Head for the Tower to the SSE first. This first Keeper will be accompanied by a few skeletons but nothing too major. Again, like the regular skeletons, the Keeper will be more susceptible to physical damage rather than magical. Kill him and then head for the tower that is NNE of where you are.
This tower should be the one floating in the air. This one is a little stranger. You will be directed to stand on a pad first. This will teleport you to the top of the tower. You will have to make your way up from there using the stairs and fighting various skeletons along the way until you get to the top. At the very top will be another Keeper. Kill him and then continue just past where the Keeper was to find another portal. Use this one to get back down but don't immediately run forward when you do because you will come out just behind the portal that leads up and if you walk forward, you'll be teleported back to the top again.
Head for the last tower. You'll have to work your way through what looks like a cemetery. You'll be attacked by a bunch of skeletons as you make your way there. Kill them and the Keeper, then return to Valerica. Talk to her and she will bring you inside the central structure.
You will enter a courtyard and then part way across, you'll be attacked by Durnehviir. Compared to some of the other dragons you may have fought, this is actually a pretty easy fight. Take him down and something odd will happen to his body. Talk to Valerica afterwards to find out what happened and then follow her to the resting place of the Elder Scroll. Take it and then leave this place.
When you get back outside, you'll find Durnehviir staring at you. He'll request that you call him to Tamriel during your travels. After your chat, head back to where you entered the Soul Cairn and make your way back up to Valerica's labs. Once in the labs, you can now use the wooden door to the balcony. Do so to get outside and then from here, fast travel back to the front of the castle and talk to the Moth Priest again.
Note: By summoning Durnehviir to Tamriel, you can learn a new shout. To summon him, unlock his shout (requires Dragon Souls) and then use the shout at the ground. This will summon him. When he arrives, he will teach you a new word for the shout. Do so three times to learn it all. You will have to wait a day in between each summoning. Doing this will unlock and achievement.
*Achievement: Beyond Death
*Achievement: Soul Tear