The Beginning The orchish shaman Ner'zhul once tried to escape Draenor, but he didn't succeed because the demon lord Kil'jaeden stopped him. Kil'jaeden destroyed his body, but left his spirit alive, of which he imprisoned in a block of ice. Kil'jaeden granted him massive power. Ner'zhul was still alive, and the Lich King was created.
Birth of the Scourge The Lich King was tasked with a job of weakening the world in preparation for the Burning Legion. The Lich King needed an army, and therefore started to create an undead army, the Scourge. The demon lords sent dreadlords to make sure that the Lich King did what he was tasked to do. The Lich King tried to experiment with his powers from within the Frozen Throne, he enslaved the local life forms, the creation of the undeath plague, which transformed everything into undead who obeyed his commands.
After gaining enough power, the dreadlords ordered the Lich King to commence the promised plan. The Lich King used his telepathy in hope to get in contact with any dark soul in Azeroth. Kel'Thuzad answered his call, and he was then enslaved by the Lich King. Kel'Thuzad formed the Cult of the Damned, and together with the dreadlord Mal'Ganis, he began the final preparations for the invasion to come.
Meanwhile, Ner'zhul, aware of Kil'jaeden's schemes, secretly sought a way out of his prison.
Invasion of Lordaeron
The following events can be experienced in Warcraft III: Reign of Chaos and the expansion, Warcraft III: The Frozen Throne.
With the Cult of the Damned and Kel'Thuzad's preparations, they launched the assault on Azeroth. The entire northren Lordaeron was consumed by the undead and the plague was spreading fiercely. King Terenas' only son, Arthas Menethil, together with Jaina Proudmoore and captain Falric took up the fight against the undead.
Arthas succeeded in killing Kel'Thuzad, as was the Lich King's plan, but his death didn't matter, as the number of the undead army increased by the seconds. Ultimately making Arthas frustrated, leading him to some unnatural decisions - he ordered the entire city of Stratholme to be purged, while the infected citizens still were humans. He encountered Mal'Ganis in city, but failed to slay him, he escaped to Northrend, where he told Arthas he would be waiting for him. Some men loyal to Arthas finally told him he was losing his mind, even his close friend, Jaina Proudmoore.
Arthas didn't stop though, he travelled to Northrend in hope to stop the scourge once and for all by killing its supposed leader, Mal'Ganis. On Nothrend, he ecnountered an old friend, Muradin Bronzebeard, whom led Arthas to a legendary weapon, in hope that it would save his people. On the way to the weapon, they encountered several enemies and sign of that the blade was cursed. However, Arthas had already fallen for the tremendous power of the Lich King. Believeing that it would help him save his people, Arthas took up the cursed runeblade, Frostmourne. Though the sword granted him extreme power, the cost was high, Muradin was (supposedly) killed when the icy tomb encasing the runeblade was shattered, Arthas began to lose his soul, eventually resulting in him becoming the first and greatest of the Lich King's Death Knights.
Arthas finally got his revenge upon Mal'Ganis, removing one of the Lich King's most dangerous jailers, but it was too late, the runeblade had already torn too much of Arthas's sanity apart. He rode off in loneliness and became a loyal servant to the Lich King. He later led the Scourge against his own kingdom, Lordaeron. Arthas started with the murder of his own father, King Terenas, and crushed Lordaeron with his newfound unholy strength.
Betrayal of the Burning Legion The Lich King was ordered to resurrect the Summoner of Archimonde, who turned out to be Kel'Thuzad. Arthas was sent to Quel'Thalas with the remains of Kel'Thuzad, he used the Sunwell in the high-elven city Silvermoon, to resurrect him.
After the resurrection, Arthas and Kel'Thuzad ventured forth to Dalaran, in order to reclaiming a spellbook of Medivh, which contained needed incantations for Kel'Thuzad in order to summon Archimonde. After claiming the book, they summoned Archimonde outside of Dalaran. After his summoning, the Lich King was no longer needed for the greater scheme, therefore he immediately gave the dreadlord control of the Scourge, but in his eagerness to fulfill their plan to conquer Azeroth, he forgot to remove the Lich King's power, meaning that the Lich King now was a powerful free roaming entity with no masters.
Illidan Stormrage was released from his ten thousand years of captivity during the Legion's invasion of Ashenvale. The Lich King knew Illidan's addiction to magic, so he realized the potential of luring Illidan to the powerful artifact, the Skull of Guldan. The Lich King therefore ordered Arthas to Kalimdor, so that he could convince Illidan to claim the skull for himself in order to repel the Legion's invasion of his homeland. With the increased power gained by the Skull of Guldan, Illidan killed Tichondrious, one of the dreadlords. Which ultimately resulted in Archimonde's annihilation at his assault on Mount Hyjal.
Failed Assault on the Lich King Illidan was confronted with the demon lord Kil'jaeden, whom tasked Illidan to destroy the Lich King in exchange for incredible power. Illidan accepted the offer and went on a quest to retrieve the much needed power to fulfill his task.
Using his demonic power from the Skull of Guldan, he awakened the sleeping naga at the bottom of the sea, and retrieved the Eye of Sargeras. Illidan used the Eye to cast a destructive spell that shattered the Lich King's defenses. However, the spell was interrupted in the last seconds by his brother, Malfurion Stormrage, he feared that the spell would cause great damage to the world. If not for the interruption, the Lich King would have been destroyed.
The Lich King When Ner'zhul pushed Frostmourne from the Throne, he had caused a crack within the icy tomb. Illidan's spell had exposed this crack, causing the crack to worsen, and now the Lich King's powers were rapidly seeping out from the tomb. Arthas was also losing his powers, since Arthas got his power from the runeblade Frostmourne, which is a part of Ner'zhul.
Knowing that the Lich King's power was weakening, Kil'jaeden sent his agents to destroy him. The Lich King sent his greatest warrior to aide him, Arthas. Weakened, but determined to save his master, Arthas reached Northrend only to find Illidan's naga and blood elves waiting for him. He raced against Illidan's forces to the Icecrown Glacier and defend the Frozen Throne.
Illidan was waiting for Arthas at the foot of the Frozen Throne. They commenced in an intense battle, which Arthas ultimately rose victorious from. As he was ascending the stairs to the Frozen Throne and his destiny, his mind was flooded with voices of those he had forsaken. Ignoring the voices, he continued the ascend to the Throne. When he finally reached the pinnacle, he saw an icy cask, within which was a suit of armor. Now only two voices spoke to him - Medivh's warning to Jaina and the rasping whisper of Ner'zhul:
With a furious cry, Arthas thrusted the icy tomb with Frostmourne, with a haunting scream, the Frozen Throne exploded. With Ner'zhul's thorny helm lying at his feet, he picked it up and crowned himself with the powerful artifact on his head.
"Your young prince will find only death in the cold north."
"Return the blade...complete the circle...release me from this prison!"
In that moment, the souls of Arthas and Ner'zhul merged into one, and inhabited the body of Arthas, and so forth, one of the most powerful entities on Azeroth was born.
"Now... we are one!"