How Did Constantine Finally Fix The Timeline?
Constantine had to return to the moment in 2018 New Orleans where he forced Desmond to break up with him. This actually resulted in three John Constantines in the same place: the original John from that moment in time who didn't break up with Desmond and left to go to the store; John the Legend who was there to break up with Dez; and the John from the future who had come to fix the timeline. Complicating matters, Charlie (who selfishly didn't want to lose her powers when the timeline is restored) shapeshifted into Ava and told Sara that Constantine was a fugitive so that the Legends - who again, were bloodthirsty against fugitives because Constantine had never joined them - arrived in New Orleans to kill John from the future.
However, it all worked out the way it had to: John the Legend broke up with Dez but John from the future intercepted Dez outside of his apartment, managing to stall him long enough so that the original John returned from the store and ran into Dez. With future John watching, Desmond and the original John kissed, thereby restoring time. This happened just in the nick of time, too, as the fire and energy blast Rory and Ray had shot at future John was just about to kill him. When the timeline was reset, the Legends also captured the Dybbuk, which was still on board the Waverider and trying to murder the heroes while possessing the body of puppet Martin Stein.
Although he reset the sequence of events that doomed Desmond, the timeline is back to the way it was. For his part, Constantine finally had a long and overdue conversation over whiskey with Sara where he fessed up about the mess he made and about Neron. Meanwhile, Charlie had realized that her selfish desires to remain a shapeshifter weren't as important as reality itself. Zari forgave her, noting that every other Legend had also jeopardized time for selfish reasons at some point.
What Is Neron's Plan For Project Hades?
The Legends may be back in business but "Legends of To-Meow-Meow" ended with a huge shock: Neron is not only on Earth but he takes the form of Desmond and is golfing buddies with Hank Heywood. Hank apologized to Desmond/Neron about the delays in Project Hades, so Neron also is apparently the entity at the head of Project Hades, which makes sense as a convergence of the two main threats of season 4. But as for what Neron ultimately needs the fugitives to be "cooperative" for, that remains a mystery to be solved. It's possible the fugitives are part of Neron's scheme to take over Hell or he needs them to steal souls on Earth to give him more power to realize his ultimate goal.
However, while Desmond showed his true demonic face, it's not yet confirmed that this is indeed Neron - it could be a demonized Desmond working on Earth as an agent of Neron, similar to how Nora Darhk was a vessel for Mallus last season. Time - and the remaining 8 episodes of season 4 - will ultimately tell when Legends of Tomorrow returns in spring 2019.