You must learn the basics and spend time doing simple examples and proofs to increase your understanding and confidence. By studying other people's proofs and truly understanding them, you learn methods of problem solving. Summary Problem solving is hard work. Learning to solve problems is learning how to think logically and creatively. The ability to solve a problem is basically a self-taught discipline requiring much work, time and frustration.
Presentation is the end result.
An elegant solution is worthless without a rigorous presentation. Learn to be rigorous at all times. Basic Elements of an Argument Understanding the basic approach to any problem will help in solving problems in general. Determine exactly what you must prove. These are the specific pieces of data relied upon to prove your goal.