It can oftentimes prove helpful to browse reference materials as a way of finding a topic for research that is of personal interest. One way to find reference material is to browse the Reference Collection in the 410's.
Another approach would be to search Library Search using the term Applied linguistics -- Research -- Methodology or Linguistics -- Research -- Methodology. Some recommended books include:
Projects in Linguistics: A Practical Guide to Researching Language by 
Doing Second Language Research by
There are now many introductions to language research available. What makes Doing Second Language Research different and special is that it puts you inside the research process. It does this by giving you different roles within a variety of mini-studies. This means you can get a feel for what it's like to be a research subject, research organizer, research data collector, research data analyst, and research reporter. All of this ismeant to help you prepare for the final goal of designing your own research. The book is organized into four parts: - Part One is a general introduction to the nature of research. - Part Two covers qualitative research and contains chapterson case study research, introspection research (use of verbal protocols), and classroom research (interaction analysis). - Part Three covers quantitative research and contains chapters on descriptive statistics research (survey analysis), correlational research (into language learning and teaching attitudes), and quasi-experimental research (into vocabulary learning techniques). - Part Four consists of a concluding chapter on course evaluation andcombining research types. Like other books in this series, Doing Second Language Research is designed to bridge the gap between theory and practice. To help achieve this balance, each chapter is organized into the following sections: 1. Introducing theresearch type 2. Experiencing the research type 3. Compiling the data generated by the research type 4. Analysing the data generated by the research type 5. Designing the research type 6. Interpreting the research type 7. Significance of the research type 8. Reflecting on the research experience Two of the chapters (2 and 8) also have sections on reporting research results. There is a content summary at the end of each chapter, numerous exercises with an accompanying answer key, and a glossary of key terms.