After learning that you need the other two Elder Scrolls to complete the reading of the Prophecy, you receive the quest:

Seeking Disclosure

The Objectives for it are:
Find the Elder Scroll (Dragon)
Find the Elder Scroll (Blood)

There are a total of three elder scrolls. The third is Elder Scroll (Sun) which is the one from Serana.

Finding the Elder Scroll (Dragon)

Scenario I - Already Found the Elder Scroll Dragon
You may have already found the Dragon Elder Scroll as it is part of the original main story. In this case, the quest objective will immediately update to "Completed"

Scenario II - Never Had the Elder Scroll (Dragon) Before
If you never found the Elder Scroll in the first place, you will start the quest Scroll Scouting that will take you to the College of Winterhold where you talk to Urag gro-Shub. This will start a new Daedric quest, the one in which you find the Elder Scroll Dragon. For a full walkthrough of that quest, see here:
Skyrim Discerning the Transmundane Walkthrough

Scenario III - Had the Dragon Elder Scroll, but sold it to librarian in College of Winterhold
If you did previously find the Elder Scroll (Dragon), but donated/sold it to Urag gro-Shub earlier when you no longer needed it, do not panic. You can just buy it back from him. The quest Scroll Scouting will commence. Go talk to Urag at the College of Winterhold Arcanaeum. Tell him you want to buy back the Elder Scroll. He asks for 4,000G for it. If you are Arch-Mage however, it will only cost you 2,000 gold.

Finding the Elder Scroll (Blood)

Speak to Serana. She has an idea of where to find the last Elder Scroll. We need to find Serana's mother, Valerica. Serana says Valerica gave her a hint: "She would go somewhere safe, somewhere that my father would never search". Serana does not think Valerica sealed herself underground or went to hide with the Dawnguards. But the idea that Valerica is hiding in Castle Volkihar does make sense. There is a courtyard in the garden, which Valerica used to tend to. Ingredients for potions came from that garden. The garden is a peaceful place which Lord Harkon wouldn't think of looking in. Serana suggests that this could be where her mother, Valerica, is hiding.

This begins the quest, Chasing Echoes. In this quest you will find the remaining Elder Scroll (Blood).