By problem solving I understand:
1. Understand what the problem demands
2. Find out edge/special cases
3. Work out examples
4. Devise a solution to the problem.
I am not implying merely reading a book will make you a problem solver. Problem solving will make you good at problem solving.
Have you come across any book that helped you become good at problem solving?
There's books like 'Art of Problem Solving' or Polya 'How to Solve It' but they make sense only after you get some experience.
Another book is TRIZ.