When Pigs Fly

"Lily Evans normally considered herself fairly even-keeled. She was level-headed, logical, and most of the time, didn't let much get under skin. Except James Potter. He had seemingly burrowed right in and set up shop." Starting with a (declined) invitation to the Yule Ball and moving forward from there, how did James and Lily become parents to the Savior of the Wizarding World?