At least for me, writing a research plan was very useful for my actual research. I found this article helpful: http://sciencecareers.sciencemag.org/career_magazine/previous_issues/articles/2002_07_26/nodoi.4611149009600202486
The book "A PhD is not enough" has some good advice for writing research plans as well.
The introductory chapters to the book "An Introduction to Scientific Research" by E. Bright Wilson will probably be helpful to you too. Specifically the advice on literature searches is good. Start with general accounts (encyclopedias or survey articles), and then move to research papers. Advice from experts in your field is usually (but not always) helpful. Applying new methods to old problems can be fruitful, although in the long run it is better to be problem oriented; ie to aim to attack specific problems by whatever means necessary.
Polya has several books on problem solving that are quite good, but fairly general. "How to Solve It" is definitely worth reading, and "On Mathematical Discovery" is very interesting as well. You should definitely look at the first chapter of "Mathematics and Plausible Reasoning"---it's short and free on archive.org.
Another general piece of advice when carrying out your plan is to try to make a minimum working example/prototype. Avoid prematurely optimizing and instead cut the shortest path towards something that works. (Think like this: to get to high ground, always walk in the steepest direction; to prioritize the steps in your plan, look for the fuzziest parts, or the parts that would kill your argument.)
You'll probably waste a lot of time and explore a lot of dead ends, although later on that experience might prove useful.
If you feel aimless, try to discipline yourself to use a notebook and state your hypothesis explicitly, then record the essential facts of your plan to test your hypothesis/solve your problem etc. It's important to record your intentions and try to make your hypotheses explicit, so that you don't keep exploring the same dead end. Pretend you're doing lab work, even if you're not.
Anyway, these are a few things that I found helpful from time to time. Good luck! Keep at it :)