The first step is generally validating the idea - fleshing it out from "vague idea" to something that starts to identify the benefits that you expect to get from the project. In such a step, this is no different from any project - it isn't unique to IT projects. Once you have an idea of the benefits, you can start to think about the project methods, structures, resources, and so on, which will also help you to think about the team.
As with any project, I would want to get a strong sponsor or executive to take ownership of the project and drive it forward at a senior level, gaining support from other senior managers, ensuring that it gets proper buy-in.
In terms of documenting the project, that will depend - at least in part - on the approach you plan to take to delivery. Agile methods are different from traditional waterfall methods, but are no less rigorous, in my opinion.
Try Googling "Project Initiation" to get some ideas of how to handle the process in different types of project environment.