There's a part of the UK's business ministry, BIS, which provides expert guidance on public dialogue, as well as promoting and supporting dialogue projects. The Sciencewise Expert Resource Centre has supported dialogues on a wide range of science and technology subjects, including nanotechnology, hybrid embryos and how to make the shift to low-carbon energy sources. There's a set of principles to guide people who are setting up a dialogue, so they can keep it open and multi-directional. Crucially, there needs to be a policy 'owner' in Government who will use the outcomes of the dialogue to help form policy.
Plenty of case studies are available on the Sciencewise-ERC website. Since every project has to be independently evaluated, there are also evaluation reports. And there's a team of Dialogue and Engagement Specialists (I'm part of this team) to advise.