The oxidation number for an element can be based on the number of electrons it needs to  to have a full valence shell. For example, the oxidation number 3- means that the element has  valence electrons and that it will gain  electrons to have a full valence shell. This will cause this element to become a  charged (-3) ion.

The oxidation number for an element is indeed based on the number of electrons it needs to have a full valence shell. In the example you provided, an oxidation number of 3- means that the element is three electrons short of having a full valence shell.

In terms of valence electrons, this element would have 5 valence electrons (since 8 electrons are needed for a full valence shell and it is 3 short).

To achieve a full valence shell, this element will gain 3 electrons.

When it gains these 3 electrons, it will become a negatively charged ion, specifically a -3 ion. This is because it has gained more negatively charged electrons without gaining any positively charged protons to balance them out.