I think that the programmer has to just start doing it. A few simple tests to start with are easy to justify as part of development.
Something like a unit test is almost always necessary to get fast debugging turn around. Just explain how much faster it is to launch the test than it is to arrange the correct input, set a debugger breakpoint, launch the application, etc.
Document the test in your code. Just put a comment explaining where the test is and how to run it. Future programmers will see it and hopefully the testing will spread!