Although think tanks "brand" the research that supports their thoughts in the media, they don't generally conduct that research themselves - they commission it from market or social research firms, or contract with independent researchers.
So, I guess the questions are about research arms of consulting firms (as opposed to research firms who offer research or analytics directly as a service).
These arms have two internal functions - they may respond to requests for research from consultants, and they can support marketing activities.
In the first role, research is focussed on gathering data to back up or guide consulting recommendations. Usually this will be secondary research unless the client wants to commission a special study.
In the second role, the research function generates "thought leadership" pieces either for senior consultants/partners to publish or for inclusion in the firm's promotional literature (which ranges from one-off brochures to regular publications like McKinsey Quarterly).
The range of roles on offer goes from researchers, through archivists and knowledge managers, to marcomms professionals.
A researcher needs to demonstrate research experience, usually through applied research in a social science field, but this does not need to be at a postgraduate level - you can become a junior researcher with a decent BSc.
Knowledge managers need to demonstrate experience on the interfaces with both IT and consultants (or the business if you have industry experience).
There may also be roles for dedicated marketing communications professionals if the firm is using its research wing to produce regular publications. They need to have communications skills and experience primarily, but also some understanding of the technical issues that the researchers will be bringing out.