How does Winston feel about the world he lives in and how it is run? What clues can you find that show how he feels?

Winston knows from the start that there is something drastically unjust about Oceania and the way it is governed. (Even this comes across as an understatement.) He hates the Party and eventually carries out a huge act of rebellion in his affair with Julia. His problem, however, is that he has no definite standard by which to judge the situation objectively. His memory of the pre-dystopia world is vague and chaotic, for he was only a child at the time. The Party has systematically wiped out records of the previous era (and does so with the present as well) and Winston has no real way of knowing for certain that life was ever any better than it currently is, or that mankind was ever governed in a way different from the totalitarian regime of the present.
His decision to keep a diary is an attempt to objectify what he knows only intuitively about the wrongness of how the world is being governed and its people controlled and oppressed as they are. At some point he realizes that much of what he's writing down is just an emotional stream-of-consiousness, a cathartic outpouring that has no intrinsic meaning beyond the pent-up resentment he feels, as he scrawls DOWN WITH BIG BROTHER repeatedly on the page. He longs for a "past" he cannot fully remember and thinks that it can be found through the proles, the working-class people whom the Party does not even consider to be human beings. Ironically, it is only through Winston's reading of "the Book," the purported work of the subversive Emmanuel Goldstein, that he begins to understand the objective reasons the Party has created and maintained the totalitarian system under which Oceania is governed (as are the other two, Eurasia and Eastasia, of the three "superstates"). Yet the Book itself, as O'Brien reveals while Winston is being interrogated and tortured, was actually written by O'Brien together with others in the regime. In these "sessions" with O'Brien that form his "reeducation" all of the truths about the dystopia that Winston only knew in vague intuitive flashes are made explicitly clear once and for all, though Winston has now been turned into an unthinking zombie, who "love(s) Big Brother."

Winston Smith is at once terrified and demoralized by the totalitarian society in which he lives. Despite the regime's best efforts at mind control, Winston still manages to retain a capacity for independent thought, which naturally leads him to want to overthrow the Party's tyrannical rule.
The most important source for Winston's true feelings is his diary. Winston doesn't want to keep his subversive thoughts all bottled up inside; he feels an urgent need to express them. But in this totalitarian society, expressing thoughts that contradict Party policy is a serious crime, punishable by death, so Winston has to be extremely careful. He figures that confiding his true thoughts about the regime to a diary is the least dangerous option, certainly much less so than telling someone about them.
Winston's diary is the only place where he can express what he really thinks about the regime. He positively loathes Big Brother; we know this because he writes "DOWN WITH BIG BROTHER" in his diary over and over again. And it's Winston's loathing of Oceania's dictator that leads him to take increasingly bold risks—such as reaching out to O'Brien, someone he believes is an opponent of the regime, but who in actual fact is an Inner Party agent. Winston wrongly thinks that O'Brien also hates Big Brother with a passion. The fact that Winston tries to establish a subversive connection to him demonstrates that his diary entries are not just words; he means to act on his opposition to the regime.
Unfortunately, Winston's brave defiance leads to his downfall. In his capacity as a Party apparatchik—a member of the political elite—O'Brien tortures Winston, not just to punish him, but more importantly to force him to love Big Brother. After his horrifying stint in Room 101, psychologically destroyed, his body broken by torture, Winston finally gives in. As he sits in the Chestnut Tree cafe, crying into his Victory Gin, he gazes up at an enormous portrait of Big Brother. At that moment, Winston, with his brainwashed mind, has triumphed over his subversive self, the self that he expressed so eloquently in his diary. In reality, this triumph, such as it is, is really a victory of the Party over Winston—and that victory is complete. For he now loves Big Brother.