Problem-solving via scientific method...

An iterative, pragmatic scheme of the four points above is sometimes offered as a guideline for proceeding:

• Define a question
• Gather information and resources (observe)
• Form an explanatory hypothesis
• Test the hypothesis by performing an experiment and collecting data in a reproducible manner
• Analyze the data
• Interpret the data and draw conclusions that serve as a starting point for a new hypothesis
• Publish results
• Retest (frequently done by other scientists)

The iterative cycle inherent in this step-by-step method goes from point 3 to 6 and back to 3 again.

Source

Other method also utilize a step by step method of problem solving.