If you are trying to use quickbuild, and the DVI viewer does not open, chances are you have an error. If you have an error, it will be visible in the log file / message area, and the summary of the error will be given.
The log file will explain the source of the error in your code. In the editor, you can use the buttons in the toolbar labeled and to jump to and from errors. The log file always states in which line the error occurred. To view the line where an error occurred, click on the error in the log window, and Kile will take you to error's line.