Your first task in the quest "Beyond Death", once you enter the Soul Cairn, is to locate Valerica. Go north/northeast on the road, following the arrow on the compass. Soon, you will see a big castle in the horizon. Go towards the structure.

Soul Cairn Side Quests
There are many sidequests inside the Soul Cairn. One of them, which you receive from a soul called Arvak, lets you get a new mount, a pretty cool one - the flaming mount.

Another one is:

Impatience of a Saint
While exploring the Soul Cairn, I've come across the soul of a strange Dunmer named Jiub. He claims to be writing the second volume of his life's story but lacks the notes from his first in order to complete it. He's asked for my help in locating the pages which are likely spread across the entire soul cairn... quite a task. (you need to find all pages from Saint Jiub's Opus, there are 10 of them).

Skyrim Dawnguard Vampire Lord Walkthrough Part 15: Jiub's Opus Pages, Arvak Flaming Mount

There is also a Soul Husk merchant who will sell you weapons in exchange for 25 Soul Husks.

It is recommended you first do the Flaming Mount quest, so that you can move more quickly in the Soul Cairn. But all these side quests are completely optional. When you are ready, continue with the main quest.

Once you reach the fort, there will be an energy barrier blocking your way, with Valerica behind that barrier. Wait for Serana to arrive. She will talk to Valerica. Then, you will speak with Valerica. Valerica tells you that when she fled Castle Volkihar, she fled with two Elder Scrolls. The scroll you found with Serana speaks of Auriel and his arcane weapon, Auriel's Bow. The second scroll declares that "The Blood of Coldharbour's Daughter will blind the eye of the Dragon". The Tyranny of the Sun requires Serana's Blood. Harkon means to kill Serana.

Eventually Valerica is convinced to help you get the Elder Scroll. You have to first help Valerica take down the barrier by destroying the keepers tending the sources of energy. She also warns you about a dragon, Durnehviir, that roams Cairn.

Check your quest log:

Beyond Death
Serana and I have located Valerica imprisoned within a massive ruin. When confronted by us, Valerica revealed that Serana's Blood is an integral part of the Tyranny of the Sun. After the reconciliation between the two of them, Valerica confessed to having the Elder Scroll hidden in her ramshackle living space. In order to free her from the prison, Serana and I will have to locate and slay the Keepers who maintain the barrier around the ruins.

Kill the Boneyard Keepers (0/3)

Use the compass to locate all three Boneyard Keepers and kill them. They are pretty far apart, so use Arvak's Mount if you have that. Then, return to Valerica. Talk to her, then follow Valerica into the Boneyard. Slay Durnehviir, the dragon, that attacks you once you enter the Boneyard. Durnehviir summons some skeletons to aid him, but stay focused on the dragon, and let Serana handle the undead adds.

Follow Valerica again, then retrieve the Elder Scroll (Blood). Talk to Valerica. If you are soul trapped, ask her if she can help you get your soul back. Valerica tells you that your soul essence was trapped inside a gem. When you and Serana entered the Soul Cairn, it was given to the Ideal Masters as payment. You simply need to retrieve the gem. The moment you touch it, your soul essence will be restored. There's an offering altar not far from here, and Valerica suspects the Soul Essence gem will be found there. Your objective now is to retrieve the Soul Essence Gem.

Note: You should get the Soul Essence Gem, finish all quests you are interested in inside the Soul Cairn, and only then leave. Some readers have reported of a bug in which you cannot enter the Soul Cairn the second time.

After you exit the Boneyard, talk to Dunehviir who is waiting for you outside. He wants to return to Tamriel, and needs you to summon him from Tamriel by speaking his name.

Offering Altar Location (Soul Essence Gem)
To find the Offering Altar, go to your quests list and then to MISCELLANEOUS. Mark the objective "Retrieve the Soul Essence Gem" as active. The offering altar is accessed by using a teleporter in a structure to the northwest of Valerica's Prison. This takes you to a roof of the building where you find a chest containing:

Soul Essence Gem (Full)

Exit the Soul Cairn from the same portal through which you entered. Once you are out of the Soul Cairn, the quest Beyond Death completes.