I'll keep this simple:

1) Laguna and Julia did not have sex; he passed out from the wine and then chatted away the rest of the night. Kiros dragged him off on a mission before anything could happen.
2) That mission was the one that ended up with Laguna, Kiros and Ward at the Centra Excavation Site, throwing themselves off the cliff.
3) Laguna washes up near Winhill and is taken care of by Raine for a year.
4) During that year, Julia gives up on Laguna, and with her heart broken, she marries General Caraway instead. They raise Rinoa until Julia dies four years later.
5) After Laguna recovers, he and Raine get together and Squall is conceived. However, before he's born, Ellone is taken by Estharian soldiers, so Laguna and Kiros go after her, picking up Ward on the way.
6) It is during the time Laguna and co. were rescuing Ellone that Julia dies in childbirth, but Squall is delivered unharmed. Squall is sent to the orphanage with Raine's surname becuase the people of Winhill didn't like Laguna.
7) Rinoa runs away from home to form the Forest Owls with Watts and Zone, dropping the Caraway name becuase her father works for the very man she despises so much, instead taking her mother's maiden name.

That's how it goes methinks.