I get this question many times, so I thought better document it.
a) Login to your twitter account from the twitter website (http://www.twitter.com)
b) Once logged in, click on your name, displayed on the top right corner and select Settings
c)This would take you to your Account settings page. Change the value in the Username field to the new username you prefer.
d) Scroll down and click on Save. You have now successfully changed your username.
Notes: After changing your username
All your tweets will be intact.
All your followers will be intact.
All the people you follow will be intact too.
Hope this helps you. Please feel free to leave a comment if this helped you.