George Lucas originally conceived the character of the Emperor as a puppet ruler, easily controlled by the Moffs. His final role as an evil mastermind is not established until we see him in person in Return of the Jedi. But while the Emperor's role in the Original Trilogy is not as explicit as his manipulation of people and events in the Prequel Trilogy, we can, in retrospect, still detect his presence behind the major events of the saga.
Episode IV: Drawing Out the Rebels
Shortly after Princess Leia's capture in Episode IV: A New Hope, Grand Moff Tarkin announces that the Emperor has disbanded the Imperial Senate. Palpatine kept the Senate alive for nearly twenty years, placating citizens with the illusion of democracy while he consolidated his power. The sudden change was, in part, a reaction to the Rebel Alliance.
The seeds of the Rebellion were sown shortly after Palpatine began to seize power during the Clone Wars, when senators such as Bail Organa and Mon Mothma worried that granting the Chancellor emergency powers would lead to a dictatorship. Over time, small Rebel groups popped up, but these were easily crushed.
It was not until two years before A New Hope, during The Force Unleashed, that the disorganized Rebel factions became the organized, unified force known as the Rebel Alliance. Now that the Rebellion was organized, they could use even a weakened Senate to their advantage. A number of senators were secretly part of the Rebel Alliance. Princess Leia, the senator from Alderaan, used her diplomatic status to run supply missions for the Rebels.
By disbanding the Senate, Palpatine the forced the Rebels out into the open. The Empire now had the Death Star, a superweapon with the ability to destroy planets, and the Rebels could no longer hide behind their Senatorial positions or strike at Palpatine politically. The Rebels only survived open military combat because the Emperor didn't count on the Rebels having a Jedi on their side.
Episode V: Finding Luke Skywalker
Emperor Palpatine's plans changed when he discovered that the Rebel who destroyed the Death Star was none other than Luke Skywalker, Darth Vader's son. In Episode V: The Empire Strikes Back, he turns his attention towards finding Skywalker and turning father and son against each other.
Here again, Palpatine's plans are foiled by his lack of knowledge. He knows Yoda survived the Jedi Purge, but not that he'll become Luke's teacher. As far as the Emperor and Darth Vader know, Luke was briefly instructed by Obi-Wan Kenobi before Vader killed him. Even though Yoda warns Luke that he is not ready to face Vader, he is much more prepared than Palpatine expected. Vader is able to defeat Luke, cut off his hand, and reveal the secret of his parentage, but not to bring him to the Emperor.
Episode VI: Laying a Trap
But, as we've already seen, Emperor Palpatine is the master of Plan B. In Episode VI: Return of the Jedi, he is able to use the Empire's defeat at the first Death Star and Luke's Jedi training to his advantage. Palpatine sets a trap for the Rebel Alliance, letting them know that the Death Star is not fully operational and that he will personally be there to supervise. With a chance to destroy both the Empire's superweapon and the Emperor himself, the Rebels have no choice but to attack and Luke has no choice but to face Darth Vader once more.
Everything about this final battle is carefully calculated. The second Death Star is visibly unfinished, in contrast to the imposing presence of the first superweapon. The path to the core is wide enough for the Millennium Falcon to fly through, rather than the two-meter exhaust port the X-Wing fighters faced in A New Hope. Tthe position of the Death Star's shields on the Forest Moon of Endor makes them appear an easy target for the Rebels to disable. And from the Emperor's throne room, Luke can see the trap set for his friends, allowing Palpatine to manipulate his feelings of hopelessness and anger.
Palpatine is at an advantage here because it doesn't really matter whether Luke or Vader wins their final duel. If Vader kills his son, he only grows stronger in the dark side of the Force -- and cements Palpatine's hold over him. If Luke kills Vader, Palpatine gains a new apprentice and a moral, as well as military, victory over the Rebellion.
Aftermath: Palpatine's Downfall
The Emperor's plans are ultimately foiled by his overconfidence. First, he does not consider the ability of the primitive, teddy bear-like Ewoks to launch an attack on the Death Star shield. (To be fair, neither did the Rebels.) Second, he does not consider that Darth Vader may still have good in him. Luke's plan to bring Vader back to the light side of the Force may appear naïvely idealistic, but he's able to touch something within his father that Palpatine thought was long gone.
Emperor Palpatine's role in the Star Wars Original Trilogy showcases both his ability to plan long-term, complicated events, but also to think on his feet. He's not only an excellent predictor of people's behavior in the situations he engineers, but can adjust his plans to accommodate multiple outcomes. His ultimate Plan B comes in the Expanded Universe comic Dark Empire, where he cheats death by projecting his essence into a cloned body. Although his role in the Original Trilogy is much more subtle than in the Prequels, he remains a frightening and devious behind-the-scenes villain.