How do active researchers start and solve a scientific problem? There are different researchers working on different subjects. I was wondering how do they find out an "interesting" problem and then solve it. This question may sound very vague. I am PhD student in Theoretical Physics. I just wanted experienced researchers (preferably from science) to share their ways to solve a problem. By this I mean :


How do they start working on a particular problem?
Once they are convinced that that problem is interesting how do they go about solving it. 


I understand there is no unique way and different people have different style of working. But I think the collection of answers will definitely help budding researchers, like me, who can get different ideas and choose their own ways out of those.   

Edit : To summarize, suppose someone from theoretical science background wants to write a single author paper, how should he/she go about it (in your opinion)?
As Jeff pointed out in his comment, there's no one answer here -- it's fairly dependent on your field. But here's my stab at a very general overview:


Read a large number of papers in your field. I like to focus on the most recent ones and then read backwards as needed to acquire background.
Make note of the "open research problems" identified in these papers (usually discussed near the end of the paper as future work).
Repeat steps 1 and 2 until you have a nice list of possible paths.
Discuss your list with your adviser (if you're a student, at least).
Be prepared to repeat step 3. Numerous times.
Eventually, you'll find something to investigate.


At that point... defining the "end" of the project is much messier and field-dependent. For my field, computer engineering, the "end" might be a working software prototype that I can evaluate in terms of performance. It might be a theoretical model that I then intend to try implementing. Or it might be something entirely different. (If I were to be cynical, I'd say that the "end" is whatever you promised in your funding proposal ;-)

As to how to get to that end -- that's the research, and it's almost entirely field dependent. Talk to an adviser or researcher in your area.

Also -- don't be so quick to aim for a single-author publication. Often times, the big interesting problems are just that -- big. They'll require multiple researchers working in tandem. And if your worry is prestige - the paper describing the first observation of gravitational waves had over 125 authors, including 3 who were deceased at the time of publication. I highly doubt anyone considers that paper to be less prestigious on a C.V. because of that :)