Janaka tells Vishvamitra how he found her: ploughing the ground for a sacrifice, he saw a baby girl rise from the earth beneath the ploughshare, and called her Sita, the furrow, for the way she was born. Sita tells it herself to Anasuya in the forest: covered in dust from the field, she was lifted by the king, and a voice from the sky told him she was his own daughter.
The Ramayan of Valmiki, tr. Ralph T. H. Griffith (Project Gutenberg 24869)
Long before the epic, a hymn of the Rigveda calls on auspicious Sita, the furrow, to come near and give good crops and rich harvests, with Indra and Pushan guiding her. Later ritual texts make this Sita the wife of Indra or Parjanya.
Rigveda 4.57, tr. Ralph T. H. Griffith (Wikisource); Sita (Wikipedia)
Sources: The Ramayan of Valmiki, tr. Ralph T. H. Griffith (Project Gutenberg 24869); Rigveda 4.57, tr. Ralph T. H. Griffith (Wikisource); Sita (Wikipedia)
Hanuman leaps the ocean to Lanka, passing the mountain Mainaka, the serpent mother Surasa and the shadow-catcher Simhika, searches the city by night, finds Sita in the Ashoka grove and gives her Rama's ring, then lets himself be caught and burns Lanka with his own tail.
At Janaka's court in Mithila no king can lift the bow of Shiva that is Sita's bride-price; the young Rama lifts it, strings it and breaks it in two, and wins Sita. Tulsidas sets it at a crowded contest, and brings in Parashurama, furious at the sound.
On the first night of the exile Rama reaches the Ganga at Shringaverapura, where the Nishada king Guha welcomes him and ferries him across. In Tulsidas the boatman will not let him into the boat until he has washed his feet, in case their dust turns the boat into a woman.
After the war Rama tells Sita before the assembly that he fought for his honour, not for her; she answers him and walks into a pyre, and Agni himself carries her out unburnt; later tellings say the woman in Lanka was only her shadow and the real Sita had waited in the fire.
Cast off by Rama because of what the people said, Sita bears twin sons in Valmiki's hermitage; when the boys sing the Ramayana at Rama's sacrifice and she is called to swear her purity again, she asks the Earth to take her, and the ground opens.
Rama worships Shiva as a linga on the island of Rameswaram — before the bridge in the Ramayana, or after Ravana's death to expiate the killing of a brahmin in temple tradition, where Sita's sand linga and Hanuman's linga from Kailasa stand side by side.
Rama wishes to worship Shiva on the island before crossing to Lanka, or after killing Ravana, to be cleansed of killing a brahmin.
Vishnu offers a thousand lotuses and his own eye at Kashi; Rama raises a sand linga at Rameswaram before crossing to Lanka; the full record is I-10 in the interactions file.