In broad strokes? Select employees carefully. Give them a reason to care about what you do. Mold the company culture such that caring (and related things, like personal authority to effect change) is prioritized over other goods which would get in the way (such as getting the most efficient outcome 100% of the time). Make it obvious to your employees that it matters to them that they fit into that culture, in the way that it matters at some companies that they file the TPS reports on time.

As a customer? Vote with your dollars in favor of businesses which invest in customer service. Most people don't, and the market gives them exactly what they really want.

Quick tip for getting what you want from companies? 1) Buy a share of an index fund. 2) If you have any issue which can't get resolved the traditional way, send a letter on paper to their Investor Relations department. They will leapfrog over all the firewalls put in place to prevent customers from talking with people who have the authority to do anything. (A related trick: mail sent directly to the Vice President of Customer Service, Office of the CEO, etc.)