The organisational part is about how to organize your organisation, team or business to aid Self Service BI in the best optimal way. At first you need to have a clear vision on what your goals are regarding Self Service BI. What do want to achieve? Define a roadmap to achieve to meet that goal. It's better to take multiple steps than one giant step.
Self Service BI for everybody in your organisation is a tricky thing. What are the risks if everyone 'does' Self Service BI? If there are risks perhaps it's better to make a distinction between power users and casual users. It's very important defining who are casual users and who will be the power users. Power users are the users who have the responsibility and freedom developing BI solutions.
The next best thing is training your employees about Self Service BI. Understanding the principles about Self Service BI, best practices, technologies to be used, etc are important issues here.
On the technology side care should be taken for a robust BI infrastructure. The BI infrastructure should support Self Service BI as good as possible. Complex queries or queries from unexperienced users can pull down your BI infratructure. Off course select BI tools that support Self Service BI in the best possible way. To often suppliers claim that they have tooling with Self Service BI support but at the end the tooling is not intuitive and users still need support from IT.
The process focus area is about organizing the procedures and processes around technology, organisation and people. When people building Self Service BI solutions it's difficult to determine whether the report is trustworthy. So need to make sure that users can rely on datasources that is reliable. I think that you have certify data in a way that users can trust this data. Users can compare figures, counts or whatever of their reports with the certified reports, datasources or report parts (usable in mashups).
Also think about creating a sandbox where users can play, try, explore with data and the tooling.