Having worked with old school software developers for years, I have a lot of experience with the standard waterfall approach. On my own projects I prefer to use an Agile methodology.
Under standard waterfall, a lot of time is spent collecting and writing requirements before starting the project. These documents are then handed off to developers who go away and build a solution to the requirements document which is then handed off to the client.
An agile methodology uses prototypes and customer feedback throughout the process. This allows a back and forth conversation which allows requirements to change as the client and developer progress.