I recommend you read JVN's "Using the Engineering Design Process for Design of a Competition Robot" paper. Although there is no "right" way to approach the design process, it will help you gain an understanding of how it could be done.
http://www.chiefdelphi.com/media/papers/2303
Also, his 2010 build journal can show the design process in action. It's a supplement to the first paper.
http://www.chiefdelphi.com/media/papers/2360