A quick overview of George Pólyas How to Solve It. Problem solving can be divided into four separate steps: Understand the problem. Make a plan. Carry out the plan. Reflect on the solution.
Understand the problem
What is the unknown? What are the data? What is the condition? Do you understand the problem? Restate it in your own words. Can the condition be satisfied given the data? Introduce suitable notation. Draw a figure. Write it down.
Make a plan
Have you seen it before? Have you seen a related problem? Find a problem with a similar unknown. Divide the problem into simpler problems. Look at a more specialized problem or a more general.
Carry out the plan
As you carry out the plan: check each step! Can you see that it is correct? Can you prove that it is correct?
Reflect on the solution
When the solution is found: check the result! Check the solution. Can you derive the result differently? Can you use the result for another problem?