The work is a fictional essay dealing with the preamble to the events described in Tolkien's novel The Lord of the Rings, and the events themselves, in the style of The Silmarillion. The fact that those events are explored in a mere handful of pages suggests that if the events described in the rest of The Silmarillion had been written in the style of The Lord of the Rings they would have filled hundreds of volumes.
When Tolkien died in 1973, his son, Christopher Tolkien, completed this part assisted by Guy Gavriel Kay. Of the Rings of Power and the Third Age bears some similarities to Elrond's narrative in The Fellowship of the Ring during the chapter The Council of Elrond; neither divulges any details about how Arnor was destroyed and how Gondor became kingless. The closeness is perhaps intentional; as Elrond told the Second and Third Age through his eyes, the Silmarillion is supposed to be told through the point of the view of the Eldar.
As the name implies, the events of the essay are focused around magical artifacts: the Rings of Power.
However Sauron's plan failed: the elves discovered his plot and discarded their Rings until they could be shielded from his influence. Sauron then waged war upon the Elves. He captured all the Rings of Power except three. While many elves were killed and the kingdom in Eregion destroyed, the Men of Númenor helped the elves and repelled Sauron. After the war, Sauron distributed seven rings to Dwarves and Nine to Men. Hundreds of years later, the Men of Númenor decided to capture Sauron to demonstrate their might. As it is described in Akallabêth, Sauron was brought to Númenor as a slave; however, he soon corrupted most Númenóreans, encouraging them to replace their traditional reverence for Eru Ilúvatar with worship of Melkor, or Morgoth, Sauron's previous master. Under Sauron's influence, the Númenórians decided to challenge the Valar by invading Aman. As a result, Númenor was destroyed and sank beneath the waves.
Only a few survivors left Númenor before it was too late, and led by Elendil the Tall and his two sons Isildur and Anárion, they had settled in Middle-earth. They created realms that were governed in Númenórean style: Elendil ruled over Arnor in the North, and Isildur and Anarion ruled together in the great country of Gondor in the South. However, Sauron survived the disaster too, and although he had lost his fair appearance, both he and his One Ring returned safely to his stronghold of old in the land of Mordor.
Years passed, and Sauron, who had renewed his might, decided to attack the new realms while they were still weak. His onslaught failed, however, and Elendil, his sons, and the Elven kings fought back. For many years the great coalition (The Last Alliance of Elves and Men, as it became known) besieged Mordor. At last the host broke through to Sauron's fortress Barad-dûr. The mighty king of the Elves, Gil-galad challenged Sauron to a duel, but he lost. Then Elendil fought him, and died too; however, he managed to defeat Sauron. Isildur, Elendil's son approached Sauron's body and cut off his finger with the One Ring. In vain the Elven kings tried to convince Isildur to destroy the ring in the fire of Mount Doom where it was made: he took it for his own and declared that it was his and his folk's, a consolation after the enormous losses of the war (beside the death of Elendil, his father, another of those who perished was his brother Anárion, who was killed during the siege of Barad-dûr). Thus began the Third Age of Middle-earth.
Isildur himself died soon in a sudden ambush by a band of orcs, and the Ring that had betrayed him was lost in the great river Anduin. Heirs of royal blood were chosen to lead Arnor and Gondor. For a millennium, both realms enjoyed relative freedom and prosperity. However afterwards, Arnor became subject to attacks from the north-eastern kingdom of Angmar. More and more people fled from the North, and although Angmar was defeated by the beginning of the third millennium of Third Age, Arnor was no more. Its people were scattered, and its royalty decreased in number and fame; however they remained true to their Númenóreans descent. They became the Rangers of the North, protecting the paths of the North from the menace from the East.
As for Gondor, it prospered for much of the Third Age. However in the beginning of its third millennium, this began to change. Gondor was assailed by orcs and men from the nearby Mordor. For a long time, no one suspected that the same force that had driven the attacks upon Arnor was now fighting Gondor.
A thousand years earlier, several Wizards, known as the Istari, had come to Middle-earth: Curunir (Saruman), Mithrandir (Gandalf), Radagast, and others of the Istari who went into the east of Middle-earth. Although it was unknown to the peoples of Middle-earth, they were emissaries from the West, sent on behalf of the Valar to help them to obtain their freedom. For many centuries they were silent, and little was done by them apart from observation and counsel. However as the times darkened, they decided to take action against a mysterious dark force which seemed to dwell in the middle of a giant forest called Mirkwood. During the attack, the force had fled to Mordor. It was Sauron, who was previously thought to have perished. And in the same year, the One Ring was found.
Sauron made war on Middle-earth again, but Frodo the Hobbit went to Mount Doom and destroyed the Ring, defeating Sauron. After this, it was made clear that Gandalf bore the Red Ring, Narya. Galadriel and Elrond had the other two rings.