I don't know if this is actually the best way, but this is how I would do it:

Find the average x and average y to get the center.

Find the angle from this center point to each other point.

Sort by those angles.

It's a tough problem to define--for example, imagine ten points along the
circumference of a circle. Now put a point inside. How should it be
connected? In that case, I think my solution will minimize concavities and
distance between vertices, but that's not true for all cases. (Twelve points
along the circumference of a circle and twelve points along the
circumference of a much bigger circle, for example.) You'll have to think
about what you want.
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