To delete Twitter, first click the button at the top of the page. It will provide a drop down menu in which you will tap the settings options. Then, scroll down to the bottom of the page and select, 'Deactivate My Account.' Check out http://www.wikihow.com/Delete-a-Twitter-Account for details.
it's everything LoiseMATCH said except that he/she forgot to mention that after you deactivated it it gives you thirty days to permanently delete it.unless you change your mind and login within the thirty days your account will be permanently deleted.