Here is what I'd do (assuming that the task at hand is a one-man task and should be completed in short period of 1-4 days or so.)
Put a work plan to include the following:
Understand the problem carefully
Identify solution elements (math background, new tool, etc.)
Assess your current abilities vs. what seams to be required
Decide to solve the problem or not based on the above step.
If you decided that you can solve the problem given your skill set and time required, put an action plan to solve the problem, that would include:
A. Complete deficiency in background (Tutorials, books, etc.) - This may include going to a course, acquire books, download software, etc. The exact answer depends on the problem at hand. For example, there is no value in trying to learn HTML in a day to solve a design problem but you can search the net for how to convert a string date to a julian date using the internet.
B. Think about the solution given the current situation parameters now that you know the technology and produce a design with success scenarios and constraints (time, size, etc.). If you got stuck on a detail (e.g. how to write Regex to parse ISBN number, ask colleges if they are cooperative or go ask the net or look it up in a book).
C. Assess your solution and see if it is the best (Search, discuss, etc.)
E. Build a working version and debug until it works as designed
If when run as designed you don't get what you want (as in B), Go TO B again Else Buy everyone lunch and call it a day :).