After talking to Serana, you will be directed to go around the side of castle Volkihar. Just outside, go off the bridge and go right. Follow the coast to find another section of the castle by some kind of dock. Around the dock will be various Skeletons. They will be very resistant to your Life Drain magic but very susceptible to your melee attacks. Make your way up the stairs to the top and you'll find a wooden door. Go through the door to enter back into the castle.
Be careful in the undercroft, you'll encounter numerous feral vampires and their various minions. Follow the path until you come to a room with canals and bridges. Make your way along this room, fighting off the Hounds that come at you. Head north all the way and up the stairs. Go west and up more stairs into a small room. Pull the lever here to lower a bridge. Go back down both sets of stairs and then immediately head west.
You'll only be able to cross half of the bridge. When you get to the middle, turn left and go through the doorway. Go down the small hall and it will turn left, leading to a room with more hounds. Go into the room with the piles of bones.
This room will wrap around to the left and lead up some stairs. Cut through the webbing at the top. You'll come to a room with a Giant Frostbite Spider. Kill it and then activate the lever just beyond it to lower the next section of bridge. Go back to the bridge and cross the rest of the way
Go up the stairs on this side and they will take you to the Volkihar Courtyard.
In the courtyard, you'll find that the Moondial has been damaged. You'll need to repair it with the missing phases of the moon before you may proceed. You will find all three pieces outside in the courtyard, not inside the building though you may explore there if you'd like.
The first piece of the Moondial is to the NE on the raised walkway. Just go up one set of stairs, grab the piece and then down the far side. The second piece will be in the small pond to the NW and the third piece will be hidden against the wall at the back of the small cemetery here.
When you go back to the Moondial, place the pieces on the empty circles of the moondial. When all the pieces are back in place, the moondial will turn and reveal a set of stairs leading down. Go down the stairs and through the door into the Volkihar Ruins.
Inside, go up the stairs to the dead end wall and pull the chain on the left.
Go into the next room with the bloodied table. Follow the stairs to the East as they go upward. This will lead to a dining area with a large group of skeletons. Kill them all and then go up the stairs to the odor at the South side of the room.
Go up the stairs here and you'll enter a room with lots of spider webs. A Gargoyle or two will attack you in this room. Continue south and go through the door there. Go up the next set of stairs and kill the two Skeletons there. Go up the large set of stairs to an area with another Gargoyle. Kill the Gargoyle and then turn around so that you are facing ENE. Go under the ruins and up the stairs.
At the top, take a left and enter the next hallway. Go up the stairs in this room and at the top, you'll find a small study area with a single door. Go through that door and kill the skeletons in the next room. Follow the path and go up the stairs until you come to another large room with a lower level. You'll encounter a couple of skeletons down there and go up the stairs at the far side of the room.
At the top of the stairs, you'll see a gargoyle in the distance. Just behind the gargoyle is a chain. You need to go up, pull the chain and then back up. The gargoyle will become real and then attack you. He shouldn't be too difficult to kill on his own. From there, head back towards the stairs down but watch on the right side for a new doorway. Go through that door and up the stairs beyond.
On the stairs, you should encounter a skeleton and at the top of the stairs will be another gargoyle. Kill both and then at the top of the stairs, turn left. You'll see a gate here with a chain to the right. Use the chain to open the gate and then go into the next room. Or, if you have the skill, pick the lock on the wooden door and this will take you around to a side hallway beyond this gate.
Either way, you should come to a medium long room with balconies on either side. Make your way up the middle and go either way to get to the side hallways. Go to the SW corner and up two flights of stairs. At the top, go through the wooden door and then go through the wooden door in the next room as well. This will take you to a room with another large set of stairs and a very large pair of wooden doors. Go inside those doors.
Inside this room, you'll be attacked by a couple of gargoyles as you cross the room. They should only come at you one at a time as long as you don't make rapid forward progress. Go up to the empty fireplace at the end of the room and turn the candlestick just to the left of it to reveal a hidden door.
Follow the long set of stairs until you come to a large room with a giant circle in the middle of it. Wait for Serana to catch up here (or go back looking for her if you think she's stuck). When she gets here, talk to her and she will tell you to look around for her mother's diary.
You'll find her mother's diary amongst the books in the small library to the W. It's a small red book on one of the higher shelves. Grab it, read it, and take it with you. Give it to Serana and she will tell you what you need to find to perform the ritual. These ingredients are scattered around the room in large bowls. Each one has a unique name so just picking up "bone meal" is not going to cut it.
The soul gem fragments are going to be along the wall just after you go up the first set of stairs. It will be sitting on a low set of cabinets in a silver bowl surrounded by other Soul Gems.
At the top of the stairs, turn left and walk past the small ledge hanging over the center of the room. This upper platform will turn left again along the other wall. Follow this as it goes towards the entrance to this room. You'll find a couple of bookshelves with ingredients on them. Walk past the first one and on the second one, you should find the Purified Void Salts right in the middle.
The last item should be on the lower floor. Go down and you should see a table with all manner of different bones sitting under the skull of a massive mammoth. In a bowl on the far left side of this table will be the Finely Ground Bone Meal.
Go back up to talk to Serana. She will add her blood and the portal will open below. Make your way down the stairs and enter. Except you'll take damage and fail to enter instead. Turns out that you're just a little too "alive" to enter. You have two choices with how to proceed. You can have Serana trap part of your soul in a Soul Gem. This will weaken you while you are in the Soul Cairn though this won't kill you. The other option is that she can turn you into a vampire, allowing you to roam through the Soul Cairn freely. The only downside to this is that you will have to do the quest to cure yourself of your vampirism before you'll be allowed to continue the quest when you return. The choice is yours.