The McKinsey Mind explains how McKinsey & Co. use a fact-based method of problem solving based on the following steps. The following is my interpretation of these steps:

1. What’s the problem? Identifying and isolating the core problem, which is usually based on a competitive, organizational, financial, or operational need.
1. Use a mutually exclusive, collectively exhaustive (MECE) approach to identify non-overlapping boundaries of the problem.
2. Break the problem down using logic trees (Visio would be great here) to show relations between components of the problem.
2. What’s probably the solution? Suggest a hypothesis for a solution to the problem, which will help guide your data gathering and analysis.
3. Analyze the data behind the problem. Determine what analysis is needed to prove the hypothesis, and just as important, determine what you do not need to do. 
1. Gather the data required for the analysis.
2. Analyze the data to prove or disprove the hypothesis. If the facts disprove your hypothesis, change your hypothesis. In other words, let the data analysis drive the solution.
4. Present the solution. If the proposed solution is bought off by whomever you are presenting it to, then the work of implementing the solution starts.