Juliet hits the Jughead core. ("The Incident, Part 2")
Daniel Faraday proposed in 1977 that the survivors try to reset time and prevent the crash of Oceanic Flight 815. He planned to detonate a bomb, resulting in the destruction of the pocket of electromagnetism under the Swan. The plan was executed, but it ultimately failed; no reset occurred.
Daniel Faraday examines Jughead for the first time ("Jughead")
As a result of time travel, several survivors of Oceanic Flight 815 were transported to 1974, during the days of the DHARMA Initiative. Daniel Faraday, a physics professor, travelled to Ann Arbor, Michigan with a group of DHARMA scientists. There, Faraday researched time travel, eventually coming to the conclusion that the manipulation of people (whom Daniel called variables) could indeed change the course of fate. Having previously seen a hydrogen bomb on the Island, Faraday reasoned that it could be used to cause such a change. Returning to the Island in 1977, he began to work at putting this plan into motion. ("The Variable")
Daniel explains his plan to Jack and Kate ("The Variable")
Reuniting with Jack Shephard and Kate Austen, he informed them of his plan. He traveled with them to the Hostiles' camp to locate the bomb but was shot to death by Eloise Hawking, his mother before he could execute his plan. ("The Variable") Jack and Kate were captured by the Others, and Jack informed Eloise (who was convinced of their veracity by Daniel's journal) of their plan. Eloise agreed to aid them with the plan, heartened by the possibility that she could undo her murder of her future son. Though Charles Widmore was opposed to Eloise taking Jack and Kate to the bomb, she did anyway, accompanied by Richard Alpert and Erik. Sayid joined the group after shooting Erik, who was threatening Kate, who then left to join Sawyer and Juliet on the submarine. Richard then led the survivors through an underwater path into the Tunnels, where the bomb was being housed. ("Follow the Leader")
Sayid removes Jughead's core ("The Incident, Part 1")
Meanwhile, on the submarine, Kate convinced Sawyer and Juliet that Jack's plan needed to be stopped. The three escaped the submarine and traveled back to the Island, with intentions to stop their fellow survivors.
Jack and Sayid, in the tunnels, removed the hydrogen bomb's core, which was all that was necessary for detonation. Storing the core in his backpack, Sayid asserted that he would be able to modify the bomb's core so that it would detonate on impact. They then left the tunnels with the help of Richard and Eloise, though Richard knocked Eloise unconscious to prevent her from accompanying the survivors any further, telling Sayid and Jack that they were on their own.
Exiting the tunnels through the basement of a house in the Barracks, Jack and Sayid donned DHARMA uniforms to fit in, and attempted to calmly leave. However, they were spotted by Roger Linus, who recognized Sayid as the man who shot his son Ben. He shot Sayid in the stomach, starting a gunfight which was ended when Hurley, Jin, and Miles rescued Jack and Sayid in a DHARMA bus. They escaped into the woods but were stopped a little while later by Sawyer, Juliet, and Kate, who wanted to end their plan. ("The Incident, Part 1") Sawyer and Jack engaged in a fistfight, though Juliet eventually broke up the fight by deciding that Jack's plan needed to happen.
Jack prepares to drop Jughead into the Swan well ("The Incident, Part 2")
The survivors arrived at the Swan site, and, after a brief gunfight, were able to throw the bomb's core into the well drilled by the DHARMA crew. However, the bomb did not detonate, anticlimactically leaving only silence for the waiting survivors. However, after a few moments of stillness, the electromagnetism in the well began to strongly pull everything metallic down the well, including some chains which wrapped around Juliet's legs as they went, dragging her down into the well also.
Though she was dragged to the bottom, the fall only knocked her unconscious, and she was able to wake up after a few moments. Mortally wounded, she noticed the bomb's core on the ground next to her. Picking up a rock, she began to hit the core with hopes of detonating it, eventually doing so after eight hits. A bright white light erupted from this detonation, sending the survivors to 2007. ("The Incident, Part 2")
Effects of the reset
The reset failed. The survivors traveled through 2007 and saw that the Incident occurred, DHARMA built the Swan, and Flight 815 crashed. Faraday's original theory was correct - whatever happened, happened. ("LA X, Part 1") Evidence suggested the reset had worked and created an alternate timeline, but "The End" revealed this timeline's true nature.