Prequel Era
He was a master during the PT and knew how to play both sides perfectly. Spread out the Jedi Order, introduce a random army at the Clone Wars that paints the Order as fools as countless troops and Jedi died in the first battle of Geonosis alone. Remember that the average citizen living on Coruscant had no idea what the Jedi/Sith were, only that it was a cult of people who never cared about them which is why the Jedi Order's public perception plummeted as the war dragged on. Paint Anakin as a caring servant of the Republic and use him as the main role model for the average citizen. Then comes the droid army and the CIS who become so feared due to introduction of Grievous which becomes the focus at the end of the war. Grievous dies, Palpatine spreads out the Jedi Order after having the CIS do the same and then enacts Order 66. 90% of the Order gets destroyed, citizens rejoice and are shocked to see Palpatine deformed as the attempt on his life has left him scarred and deformed but his resolve has never been stronger.
Original Trilogy
For the first couple years after the Empire was formed, they were mainly establishing their place as the ruling power in the galaxy (The Empire Did Nothing Wrong). Vader was active usually hunting down Jedi which Palpatine constantly felt was a utter waste of time. Palpatine devoted much of his time to Sith Magic and studying the pathway to immortality as his Master did before him. He didn't have to do anything regarding the process of ruling the galaxy once the core was set up as governors would do their duties, and if there was a problem, Vader would step in to deal with it. And that's where it went downhill for him, he was so incredibly preoccupied with unlocking the secret of immortality, that the Empire began to facture and hence the Rebels grew stronger. Then Vader realized he had a son and set up to turn him over to the Dark Side. Palpatine though he had a firm leash on Vader except that loosened once Luke steeped into the picture. At Endor, Palpatine was incredibly overconfident in his Empire's ability to destroy the Alliance but I'd bet he never suspect that his legion of troopers get destroyed by an unexpected foe. As Luke was getting shocked with Unlimited Power, Palpatine was in his own world and never thought Vader would lash out and return to the light at that very moment. He'd thought he had a grip on Vader but the moment he electrocuted Luke, it was game over as all the prior memories of Anakin came back in full force and Anakin "killed" Palpatine.
Sequel Era
Palpatine died due to horrible writing the end. He died on the second Death Star, not at the hands of a scavenger...