In 1984, how do Winston's feelings of powerlessness lead to his sense of alienation?
Winston feels powerless because (1) lack of privacy, (2) denied freedom of speech and (3) control over the past, altering the past.
In the oppressive society of Oceania in George Orwell's 1984, Winston Smith, the protagonist constantly finds himself (and his way of looking at the world) at odds with those around him. While Winston's feelings of powerlessness have a number of roots in the novel, his general lack of privacy, his being denied the freedom of speech, and the Party's control over, and ability to alter the past all serve to tighten the Party's grip on its citizens - even other Party members.
As far as elaborating on these points with specific reference to the text, it really boils down to how to interpret Winston's lack of privacy, his inability to speak freely, and the Party's control over the past in such a way that they reflect on Winston's place in the society of 1984.
Winston's powerlessness manifests itself in his lack of privacy. With the constant supervision not only of the telescreen but also of his fellow citizens, Winston feels as if he has little or no power over himself. The decisions he makes and the things he does are not his to make. This serves to abolish any sense of Winston's individuality. He does not exist for himself, his own needs are most often sacrificed to the needs of the community (the Party, specifically). Telescreens constantly monitor his actions, as do the Parsons' children down the hall. While the accusations of the children are dismissed by Winston, they do illustrate the idea that everyone is watching Winston - and this includes Big Brother.
Closely connected with the idea of a lack of privacy is Winston's inability to speak freely. Like the first point, not being able to speak freely does not allow Winston to express himself. In many ways, this also serves to alienate Winston from himself. His thoughts/views do not matter, and even more, they are actively being suppressed by the Party. Winston's only real outlet is the diary he starts in Book I. Even though it serves as his outlet, he cannot write in it freely. He is constantly aware of the telescreen and of others who would "rat out" Winston. Ultimately, this hampers Winston's ability to express himself freely.
In his job at the Ministry of Truth, Winston "rectifies" newspaper articles and other forms of communication, expunging infomation that could be damaging to the Party, particularly the public's view of Big Brother. In doing this, the Party controls the past. More specifically, they control how the public perceives the past. While this shapes the way that the public sees their past (and ultimately their present), it also reflects Winston's view of his own past. Winston questions his own memories, knowing how the Party treats the past. His uncertainty regarding his own past contributes to Winston's alienation; he becomes isolated, and even separated from his past. He cannot be sure of what is real and what is not. His powerlessness lies in his inability to bring clarity to what has become muddled for him.
Ultimately, Winston's powerlessness brings about his feeling alienated not from the world, but from himself and his own past. He is floating in a metaphorical "no man's land" where decisions are not his own, his words are not his own, and even his own past does not belong to him.
If it is not too late, I think I can help you out a bit with #1:
1. The number one reason for Winston's lack of privacy is the telescreens and mics:
Behind Winston's back the voice from the telescreen was still babbling away about pig-iron and the overfulfilment of the Ninth Three-Year Plan. The telescreen received and transmitted simultaneously. Any sound that Winston made, above the level of a very low whisper, would be picked up by it, moreover, so long as he remained within the field of vision which the metal plaque commanded, he could be seen as well as heard. There was of course no way of knowing whether you were being watched at any given moment. How often, or on what system, the Thought Police plugged in on any individual wire was guesswork. It was even conceivable that they watched everybody all the time. But at any rate they could plug in your wire whenever they wanted to. You had to live -- did live, from habit that became instinct -- in the assumption that every sound you made was overheard, and, except in darkness, every movement scrutinized." (Part 1 Chapter 1)