Analyze the cause of the fear. Find out why the fear started in the first place. Some fears, like the fear of driving, are easily placed. A fear of driving often results from a car accident or similar event that sticks in the driver's mind. Other fears, like arachnophobia, the fear of spiders, might not have known origins and often stem from observing others afraid of spiders or an event during young childhood that isn't fully remembered. Taking the time to determine what the fear is, where it stemmed from and why it persists is the first step of overcoming the fear.
Talk about the fear. Talk to a friend, family member or even a pet about the fear. This not only helps by getting the fear out in the open, but it also helps by organizing the fear. While talking about the fear, determine if the fear is justified or if it is illogical. Sometimes, determining that a fear has no logic helps get rid of the fear and trains the mind, while not actually facing the fear, until it accepts that it isn't harmful.
Confront the fear. The only way to train the brain to overcome fear is to confront it. Face the fear on a daily basis. For example, a fear of spiders is overcome by gradually facing a spider at a closer proximity every day. Eventually, the spider will become commonplace, and the fear will fade.
Avoid panicking. While confronting a fear, especially for the first time, panic is a common problem. Take a deep breath and move away from the feared item until later, and then try again. Continue this process until the panic is gone and the fear is conquered.