Winston Smith faces many conflicts during his story, but the most important come with his interactions with other people. He is a worker for the Party and therefore cannot express his wishes for change and revolution without being mentally readjusted, so at first he descends into daydreams. Only after convincing himself that there are many others who share his views does he begin to reach out.
Winston's personal conflict, that of individualism vs. collectivism, is most powerfully seen in his relationship with Julia, who is not a revolutionary in any real sense, but a pathological rule-breaker. Winston's need to rebel is mirrored in her own, but she does not care beyond the breaking; Winston wants to cause real change in the system, which he hates, but Julia just wants to have the dangerous fun. In the end, both Winston's conflict of individualism and the conflict between his passion and Julia's superficiality end in their mutual inability to remain strong under torture.
Meanwhile, Winston's desperate desire for revolution causes him to confide in O'Brien, who he believes is the secret leader of a fifth column in the Party. Winston's conflict here is that of trust; no one ever reveals his true self, so Winston must break his mental training to trust that O'Brien is on his side. This trust is sadly mistaken.
Finally, Winston's conflict with the Party itself -- exemplified by Big Brother, who follows him everywhere and gives him no privacy -- is finally resolved by elimination. There is no place for conflict of any nature in the Party, so Big Brother stamps down on Winston and forces his square peg into the proper round hole.