The Galactic Empire was a constitutional monarchy that was formed to replace the failing Galactic Republic and to bring Sith rule to the galaxy. It was formed by Supreme Chancellor Palptine, who lead the Empire to victory for many years. After his death in 12 ABY his apprentice Darth Vader became Galactic Emperor, with Luke Skywalker as his apprentice, and has ruled for over eighty years.
We stand on the threshold of a new beginning. In order to ensure our security and continuing stability, the Republic will be reorganized into the first Galactic Empire, for a safe and secure society, which I assure you will last for ten thousand years. An Empire that will continue to be ruled by this august body and a sovereign ruler chosen for life.
The Empire was said to have started when the Sith Lord Darth Sidious, whose alter ego was Senator Palpatine of Naboo, helped instigate the Naboo Crisis while using the Trade Federation as a pawn. This led to Queen Amidala calling for a "Vote of No Confidence", which helped him replaced Supreme Chancellor Finis Valorum. When his apprentice Darth Maul was killed, Sidious took former Jedi Count Dooku as his new apprentice. Dooku then helped form the Confederacy of Independent Systems, which would in turn initiate the Clone Wars.
Palpatine brought much corruption in the Senate to an end. He was thoroughly trusted and when the Clone Wars erupted the Senate happily refurbished with emergency powers. Eventually, the Senate lost most of its power and became little more than a formality that Palpatine had to go through to pass his laws. However, Anakin Skywalker found out of Palpatines true identity, he reported to the Jedi Master Mace Windu who sent a Jedi task force, including himself, to arrest Palpatine.After a brief duel, Palpatine appeared to be defeated. Skywalker arrived and demanded the Sith Lord's life be spared, that he might stand trial. Deeply troubled, Skywalker nonetheless helped Palpatine kill Windu, prompting him to be held under Palpatine's sway as his new apprentice and enforcer, Darth Vader. Palpatine then proceeded to carry out the Great Jedi Purge, which eliminated almost all of the Jedi, while simultaneously wiping out the remnants of the Confederacy at Mustafar, thus bringing an end to the Clone Wars. Secure in his power and position, Palpatine used the so-called Jedi rebellion to issue the Declaration of a New Order and declared himself Emperor of the Galaxy in 19 BBY, replacing the Galactic Republic with the Galactic Empire.
Many people under the new Empire enthusiastically supported the vision outlined in the Declaration of a New Order, largely due to the violence that had plagued the galaxy for so long. Many Senators wholeheartedly supported the new government while a number of more cautious senators chose to watch and wait to see how the new government would handle the affairs of state. It promised to trade frailty for strength, chaos for order, and uncertainty for decisiveness. In retrospect, the foundation of the Empire had already been set down during Palpatine's chancellorship and all potential threats eliminated; therefore, the transition from Republic to Empire was relatively smooth.
It is important to note that not all of the Senators liked what they saw. In fact, the Petition of 2000 sought to bring the worries of these Senators to Palpatine. This petition was led by Bail Organa, Mon Mothma, and Padmé Amidala. Palpatine's dismissal of their concerns was one factor that led Organa and Mothma to help found the Alliance to Restore the Republic.
The main body of the Empire's government was made of three branches.
Council of Moffs
The Council of Moffs was a council of Grand Moffs and Moffs in the Empire that were in charge of military operations and movements across the galaxy. They also convened at the behest of the Supreme Commander, or in order to debate, pass, or dissolve laws of inter-sector jurisdiction and taxation. Each sector had a sectorial Moff ruling over it, and the Moffs usually commanded their own Sectorial Fleets, a fleet which helped with the defense of a sector.
The Imperial Senate, while having limited legislative power, was mostly a formality to keep systems happy and justified that they still had some power in Imperial politics. The Senate could advise the Emperor, hold debates on the Imperial budget, and also pass new laws. But the Emperor had direct authority over these actions, and can choose to change or abolish them, if he wished to.
The Supreme Court was the highest court of law in the Galactic Republic, and composed the judicial branch of the Republic's government. The Supreme Court was comprised of twelve justices, including the Chief Justice, who headed the Court and the judicial branch.