How do you do a research design concept paper?
When you say "concept paper," I assume that you are talking about the sort of brief draft of a full grant proposal that you might submit before submitting a full grant proposal. Such a paper is really not that much different from a problem statement and purpose statement.
Typically, a concept paper has a brief introduction that shows that you have researched the granting institution and that your purposes mesh well with its purposes. Then you move into the "meat" of the paper. You start with a problem statement, explaining the issue that you want to address and why it is important. You then continue with a purpose statement. Here, you explain what sort of research you propose to do, telling the granter what your research questions will be. This should be followed by a description of your research design, telling exactly how you will go about doing the research.
Remember, the concept paper is generally a rather short paper, along the lines of five pages. Therefore, all of this will be relatively brief summaries and you must really distill the important parts of your project into a small space.