Please refer to any book on Product Development. Its a long process and can be not be explained in few words. However, any product development commences with customer needs. 

A classical book on Product development is "Product Design and Development", Karl.T.Ulrich, Steven D Eppinger, Anita Goyal Tata McGrawHill,

Please read through the book. If you have specific prodcut in mind then same can be discussed. In fact every product development is a challenge in itself.

Well... A Mechanical engineer should remember 3 steps while developing an innovative system.

1. A complete data on which u have to work and define the problem clearly.

2. Start with analytical analysis for basic idea.

3. Observe the theoretical results and go to possible simulation techniques to compare the data, finally proceed to experimental analysis. 

there are several books on the product design by deherst and boothroyd gothrough them

You can read engineering design to know the sequence operation of any mechanical engineering machine.