Rey, Finn, and Kylo are all siblings.

Kylo, we know already is Ben Solo, son of Han and Leia.

Finn is the son of Han and a woman he had an affair with during his rocky marriage with Leia.

Rey is the biological daughter of Leia and Ezra Bridger.

Ezra was a teaching partner with Luke and an agent of Snoke inside the new jedi academy. Ezra does not want to work for Snoke, but he is forced to because Snoke holds his love, Sabine, frozen in carbonite at a hidden location. The only way to get her back is for him to complete Ben's training in the dark side arts using knowlege gained from sith holocron he obtained on Malachor.

Snoke is not force sensitive himself at all, and Ezra is not a sith. Ezra is a grey jedi who has mastered both the light and dark side. He just happened to be the last remaining jedi with dark side knowledge. But, as a grey jedi Ezra cannot help Snoke without imbalancing the force to the dark side. So to counter this he secretly steals a lock of Leias hair from Ben who he has befriended. With some other person or medical droid's help he has an artificial egg crafted from Leia's DNA and an artificial seed crafted from his own to create Rey.

He left Rey hidden on Jakku with Unkar Plutt who he mind tricked into looking after her, protecting and teaching her a trade and ensuring she had enough to survive. He intended to return and bring her to the academy later to train her in the light side of the force so that there would be another powerful jedi of Skywalker lineage to keep the force in balance.

He did not anticipate the destruction of the academy and the disappearance of Luke.