Starting at the South Pole, move to the nearest country centroid (its geographical center). From there, move to the closest country centroid you haven't visited yet. Keep going until you've visited all 196!
Data from Portland State University (https://www.pdx.edu/econ/country-geography-data), for missing countries from CIA (https://www.cia.gov/library/publications/the-world-factbook/fields/2011.html)
Hints: at the end of each answer, you are shown the initial letter of the following answer. If the following answer has either a space or a "-" in it, the initial is followed by dots
The number in the 'D' column shows how many km you have to travel to reach the destination