How are neutral atoms converted into anions?

Anion is negative ion.

In an atom, there is equal number of protons and electrons, thus the positive charges balanced out the negative charges so an atom have no charge.

To form a ion, you must understand that only electrons in an atom are allowed to move, protons cannot move before it is held in the nucleus by strong attraction force.

Thus, to form a anion, the atom have to gain electrons. So that the ion have more electrons than protons and hence becomes negatively charged.

Extra:

Similarly, to form a cation (positive ion), an atom have to lose electrons so that the ion have more protons than electrons and hence positively charged.