It seems that no matter which Middle Earth story is being told, Sauron is inescapable. His machinations always seem to be happening in the background, even when he's not the central villain of a given story. This trend doesn't seem to be changing with Amazon's upcoming Rings of Power series. Sauron once again seems to be the major threat, though this time around it's much earlier on in his story. The show may be focusing on more of Sauron's origins, if not at the very beginning, then at least much earlier than when the audience meets him in the Lord of the Rings movies.
As one of the biggest threats to the safety of Middle Earth, Sauron has always been a main player in its history. But where exactly did he come from? What created this force of evil, and what was Sauron's grand design for Middle Earth? It will be interesting to see how much of his history the show ends up exploring, because his story is certainly a far-reaching and fascinating one.
Sauron was one of the most powerful Maiar, who were the spirits that descended to Arda to help the Valar shape the world. They were all incredibly powerful beings and included many other characters well-known to Middle Earth, such as the wizards like Saruman, Gandalf, and Radagast. Sauron was created by Ilúvatar — the highest deity — before he had even begun the Music of the Ainur, which is essentially what created the physical universe. In that sense, Sauron is older than Middle Earth itself. His name was not always Sauron in the beginning, either; he underwent a name-change, like many characters in Lord of the Rings are wont to do.
The Beginning
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Originally, Sauron was known as Mairon, and was one of the Maiar of Aulë. He was regarded as strong, surpassed only by the master Smith of the Valar, Aulë himself. Mairon loved plans and order, and did not appreciate chaos. While order can be a good thing, his obsession with it soon overshadowed his care for the living beings of Arda, and absolute order became his ultimate end goal. He became very interested in Melkor (also known as Morgoth), the greatest of the Ainur who defied Ilúvatar and fell from grace, eventually becoming one of the main forces of evil in the world.
Mairon admired Melkor's power and his ability to make all of his plans become reality in such an efficient way. He became Melkor's most trusted servant, and was known as Gorthaur to the Sindar of Beleriand and Sauron to most others. Though Sauron admired Melkor, they did not have the same vision. While Melkor wanted to totally corrupt and unmake the world, Sauron wanted to take it over and rule it, and to do as he wished with Arda and the people within it.
In the First Age, Melkor constructed his main fortress of Angband in the Northwest, and he appointed Sauron as its commander. The Valar managed to capture Melkor during the Battle of the Powers, but when they searched Angband, Sauron had managed to escape. Sauron continued Morgoth's evil plans until Morgoth was unchained and destroyed the Two Trees of Valinor, which is when Men were born into Middle Earth. Morgoth left Sauron in charge of the war as he set out to corrupt the newly-born Men.
Sauron led many attacks during the War of Wrath, but was eventually overtaken by the Host of the West (aka the good guys). After Morgoth's downfall, Sauron adopted a "fair form" and repented of his evil deeds to the Valar. They ordered him to return to Valinor to receive the judgement of Manwë, but he found the idea too humiliating, and instead fled and hid his form within Middle Earth.
The Second Age
In the Second Age (during which The Rings of Power will be set), Sauron began to stir again. He had judged that the Valar had forgotten about Middle Earth and would no longer notice him, so he once again set out on his campaign of evil. Many Men had already been corrupted by Melkor, and followed Sauron immediately. He decided to make Mordor his base of operations, and brought Elves into his service as well (since they were much more powerful than Men). He disguised himself as a being called Annatar (Lord of Gifts) as a way to get people to trust him, though more powerful beings like Elrond and Galadriel never did.
He used Elven smiths to forge the Rings of Power, because he promised them these rings would help preserve their powers over Middle Earth. Of course, in truth, he only wanted the power of the One Ring for himself. When the Elves realized what was happening, they refused to use the Rings and did not give them to Sauron, causing his War against them. Sauron began to devastate the lands of Middle Earth in his quest for power, including the destruction during the battles on Númenor.
The destruction on the island was too much, and so Ilúvatar intervened and sank the entire thing under the sea. Sauron was still on it and was caught in the flood, though his spirit survived and managed to make its way back to Middle Earth. His spirit rested in Mordor, just waiting to gain enough power to assume a physical form once again, which he did manage to do — right before having his finger (which wore the One Ring) sliced off by Isildur.
From here, his story is fairly well-known known, as it appears in The Lord of the Rings. There is no way to know for sure right now how much of his story will be told in The Rings of Power, but it seems as though he will certainly be a major player in the story once again.