Ive been involved in IT auditing and consulting for 13 years and through my experience, there is definitely a methodology that can be utilised or tailored to suite the clients environment, here are just a few high level pointers
1) Its important to initially gain an understanding of the business so yes as youve stated that would be a good starting point, document the entire business process so itl provide a clear picture of the business operations.
- Arrange a workshop with key client representatives, together with the client decide on the business processes/sub-processes that the client would like to have automated and the ones that will remain manual - Your professional judgement and advise would be key here
- Once decided on the automated processes, put together a functional specification which will detail the system requirements or what will be required from the potential software system to be implemented.
- If you know of suitable Off-the-shelf software options to suite the requirements of the func spec then highlight them to the client as suitable options or you could put out a tender inviting potential software companies to market their software product to the client, motivating how their system will meet the requirements detailed in the func spec.
That would be a good starting point
2) You could either charge a rate per hour or divide the solution as a phased approach and charge a fee per phase
Hope this helps :)