After he killed Hercules and broke the Arena floor, Kratos fell into the sewers below the arena. There, he pulled a switch which opened an underwater path and leads up to Poseidon's Chamber. In that chamber, Kratos encountered several enemies, including Bronze Talos that decorated the halls. In the far center of the chamber was a hallway that leads to a Pandora Statue, whom Kratos searched for. To get to get to the statue, Kratos cranked the wheel that gates raised, and the hallway cleared.
To the far right of the chamber was a room that contained all three Hyperion Gates. There, Kratos solved its puzzle by weighing down the elevator, using both Feral Hounds and himself, which allowed him to make his way the Poseidon Princess' Quarters. After he got Poseidon's Princess, Kratos made his way back to the center of the chamber, took her with him, where he cranked the lever once more and used the Princess to keep the crank elevated and, thereby, opened two gates.
As Kratos then proceeded to the bronze statue of Pandora, the Princess' body succumbed to the crank's weight and was crushed by its levers. While Kratos spoke to Pandora, she was brutally interrupted by Zeus, which had Kratos rush the hallway that leads outside to the Upper Gardens platforms. Those platforms then lead him straight into Aphrodite's Chamber.
That note from Poseidon was found the chambers of his princess. The note read:
Dearest beloved, I ask your forgiveness for making you the subject of my rage. It is not you who angered me so, but my brother and his refusal to harness the great power he hides within the labyrinth. A storm is brewing and Zeus provides Olympus with no harbor. Only the comforts found in your arms give me rest." -Your Lord, Poseidon
That one was found in the chamber where the Pandora Statue was, and read:
"A mere girl, somehow she is the key to the Labyrinth. I brought this statue here, but so far have learned nothing. That mortal Daedalus, in his madness, has devised a way to shield secrets from even my far reaching view. This does not bode well. I fear Zeus is no longer the brother I once knew." - Poseidon