Listen to your own speaking patterns. Use a voice recorder to record yourself. Select a passage from a book or script and read over it out loud. Listen to your accent and how it differs from your desired one. You will need to be aware of the differences before you counteract your natural accent.
Immerse yourself in an area where people speak with the accent you desire. People will often begin to mimic the speech patterns of the people around them, and hearing an accent daily will help you to change yours.
Mimic other speakers. Many people are afraid of offending other people by mimicking the way they speak, but one of the best ways of counteracting your natural accent is to copy other people.
Take classes. A number of organizations such as American Accent Training (americanaccent.com), Accent Reduction Classroom (accentreductionclassroom.com) and AccentSchool (accentschool.com) offer classes and private tutoring designed to help you produce specific accents.
Listen to the radio and watch television and films. This is useful if you can't find anyone in-person who has your desired accent. Listen to speakers in the media and try to emulate the sounds they produce.