How does an atom become a positively charged ion?

By losing electrons

Explanation: A neutral atom consists of equal number of protons and electrons, thus the net charge is zero. When an atom lose electrons, the number of protons exceed the number of electrons and thus acquire positive charge.

Sodium is an element with atomic number of 11 and thus contains 11 electrons and 11 protons. When it loses its valence electron, the number of electrons reduce to 10 and thus it acquire a positive charge.