In The Lord of the Rings: The Fellowship of the Ring, Gandalf becomes suspicious of Bilbo's Ring and travels to Gondor. Here, he sees Mordor covered in flame and ash. As such, it seems like Sauron has recently moved in, and his armies are beginning to be built. However, The Lord of the Rings books and The Silmarillion explain that Sauron had been around for much longer and is only taken seriously by most once the One Ring is discovered.
During his battle against the Last Alliance of Men and Elves, Sauron was defeated by Isildur and lost his physical form. But as long as the One Ring stayed intact, Sauron's spirit would continue to linger. Almost exactly 1000 years later, Sauron began to return to the world, hiding in the ruins of an old fortress named Dol Guldur. He could only appear as a ghostly figure and disguised himself as a dark sorcerer named The Necromancer, so no one would suspect his true identity.
Sauron built his strength for another 1000 years, during which his Nazgûl returned and began waging war on the North. His defeat at Mount Doom meant the recovery was going to take a long time, but that didn't mean Sauron sat idly. His armies were growing, and the Kingdom of Arnor was attacked by his second in command, the Witch-king of Angmar.
However, the appearance of the Nazgûl began to arouse suspicion, and Gandalf the Grey felt compelled to infiltrate Dol Guldur. Not ready to reveal himself, Sauron fled to the east for almost 400 years in hiding once more until he eventually crept back to the fortress. It was this same year that Smeagol found the One Ring in a river, although Sauron had no way of knowing his Ring was found.
Sauron continued his patience for 200 years more in Dol Guldur but was eventually met by Gandalf once again. This time Sauron was caught off-guard and discovered by the wizard, only to be beaten and driven out of the fortress. Sauron secretly fled to Mordor and continued building up his armies, as well as the construction of his tower: Barad-dûr. Peter Jackson depicted these events in The Hobbit trilogy as a condensed version taking place during the reclaiming of Erebor.
Shortly after arriving in Mordor, Sauron was finally willing to openly reveal himself to the world, and the events of The Lord of the Rings followed soon after. This means Sauron waited for around 2000 years before making his move, which is a rather respectable amount of patience. Although it means his defeat would have been even more painful to him, as all of his waiting was ultimately for nothing.