Short answers, pulled from the story.
The Galactic Empire began its rule in 18 BBY when Grand Moff Wilhuff Tarkin presented a plan to Palpatine outlining the Empire's goal and structure. This political transition followed the Clone Wars which ended shortly after Anakin Skywalker became Darth Vader.
Star Wars creator George Lucas designed the Galactic Empire to be aesthetically and thematically similar to Nazi Germany, the Soviet Union, and ancient Rome. He modeled the Empire on Adolf Hitler, Napoleon Bonaparte, Augustus Caesar, and the United States' involvement in the Vietnam War.
Grand Moff Wilhuff Tarkin utilized Imperial Stormtroopers, a massive fleet of 25,000 Star Destroyers, and the Death Star as instruments of power. These assets allowed the Empire to destroy planets like Alderaan and suppress dissent through terror rather than force itself.
The Galactic Empire no longer existed as an official government or major power by the time of The Mandalorian set five years after the Battle of Endor. A year after the battle the Rebellion defeated the weakened Empire during the Battle of Jakku and formally established the New Republic.
Palpatine desired the Empire had no clear line of succession since he intended to rule ad infinitum which created a power vacuum upon his death. Most intelligent competent and experienced military officers were killed at the Battle of Endor allowing revolts infighting fiefdoms and warlordism to fracture the Empire apart.