How does a person become "charged" as he or she shuffles across a carpet with bare feet on a dry winter day?

This process occurs because there is a contact between the carpet and the person's feet. Basically that contact generates the transfer of some electrons to the carpet on dry winter days.

In this way a person is charged when dragging bare feet on the carpet on a dry winter day.

Therefore, the net positive charge occurs on the surface of the carpet.