XKCD tackles the astronomical and geographical challenges of following the Star of Bethlehem:
If the wise men leave Jerusalem and walk toward the star Sirius, day and night, even when it’s below the horizon, this is the path they follow over the surface:
If we allow a little theological confusion and assume the wise men can walk on water, they’ll eventually wind up going in an endless circle, 30 kilometers in diameter, around the South Pole.
Re-reading Matthew 2:7-10, however, I can't quite tell who the Magi were, what star they thought they were following, or what exactly they used to ascertain when it had showed them the location they sought. Possibly someone sent up a flare from the manger?