I am looking for a book that specifically focuses on the research phase of UX. Specifically the different methods available, when to use them and how to conduct them. What should I buy?
One book - impossible!
General UX research and practical application:
Undercover User Experience Design by Cennydd Bowles and James Box.
Undercover User Experience Design is a pragmatic guide from the front lines, giving frank advice on making UX work in real companies with real problems. Readers will learn how to fit research, generating ideas, prototyping and testing into their daily workflow, and how to design good user experiences under the all-too-common constraints of time, budget and culture.
Rocket Surgery Made Easy by Steve Krug. The Do-It-Yourself Guide to Finding and Fixing Usability Problems.
Steve Krug spells out an approach to usability testing that anyone can easily apply to their own web site, application, or other product.
By paring the process of testing and fixing products down to its essentials (A morning a month, that's all we ask ), Rocket Surgery makes it realistic for teams to test early and often, catching problems while it's still easy to fix them. Rocket Surgery Made Easy adds demonstration videos to the proven mix of clear writing, before-and-after examples, witty illustrations, and practical advice that made Don't Make Me Think so popular.
Andrew Hinton reviews Observing the User Experience: A Practitioner’s Guide to User Research, by Mike Kuniavsky (Morgan Kaufmann, 2003). Although I've not read it, from what I understand it's very good.
"Measuring the user experience" by Tom Tullis and Bill Albert is an essential book for learning to collect, analyse and present usability metrics.
You might also want to check out "Understanding Your Users: a Practical Guide To User Requirements Methods, Tools, And Techniques" by Catherine Courage and Kathy Baxter.
This book contains highly practical advice for a large variety of user research techniques, along with checklists, examples, and case studies. One of my all-time favorites!
Another goodie is Nate Bolt & Tony Tulathimutte's Remote Research. Contains plenty of tips for quick and easy testing, and tips that will work with a shoestring budget. It's a quick read too!
This video from Steve Krug is a good indication of what to expect from his book and is fun to watch - http://network.businessofsoftware.org/video/steve-krug-on-the-least-you.
Designed for Use by Lukas Mathis
It is a really good overview of usability and many of the books already listed here. It includes numerous links for every chapter, for when you need more in depth information. It is one of the few books that supports its advice, while still being an enjoyable read.