How does the Party use fear to control people?

Fear is the main way the Party controls its members. The Party uses fear because it knows that if people are obeying it from fear rather than their own choice, the Party has power over them. The (secret) goal of the Party is the maximize suffering in order to demonstrate its power.
Because it puts such a premium on fear, the Party has come close to perfecting this form of control. On a macro level, the Party fosters constant fear of dangerous outsiders, be they whatever rival superpower with which the country is at war or subversive infiltrators like Goldstein.
On an intermediate level, posters constantly remind people that Big Brother is watching them, while memory holes punctuate office buildings at frequent intervals so that people can get instantly get rid of any scrap of documentation that differs from official Party doctrine. In addition, people frequently "disappear" without a trace and are treated as if they never existed.
On an individual level, people know that they are constantly being watched, even by their own children, and that any instance of unorthodoxy or thought-crime will be severely punished. You can trust nobody. Even the words you say in your sleep can be used against you.
People live in chronic fear, too, because there are no laws. Therefore, anything they do or think can be construed as a crime. They have no grounds on which they can say their behavior was within the confines of the law.

The Party members of Oceania live in constant fear of being arrested, tortured, and publicly executed for thinking, discussing, or plotting against Big Brother. The Party maintains a stressful atmosphere, where members are under constant surveillance and the Thought Police spy on their every move. No citizen is exempt from the watchful, ever-present eye of Big Brother. Citizens like Winston Smith cannot trust anyone and need to make sure that they appear completely orthodox at all times. The strategically placed telescreens also add to the intimidating presence of the Party.
The Party also uses the foreboding Ministry of Love to threaten and strike fear in those contemplating dissent. The Party members are aware that dissidents are tortured in the basement of the Ministry of Love and the armed guards standing outside the massive structure send a threatening message. The Party's public executions and concentration camps are also deterrents that strike fear into the population. Overall, Big Brother creates a hysterical, oppressive environment where the Party members live in constant fear of being tortured, publicly executed, or sent to work in concentration camps with other political prisoners.