How do polyatomic ions get their charge?

have a charge because they have more or fewer valence electrons than the neutral atoms that make up the ions.
The most common polyatomic cation is the ammonium ion, ##”NH”_4^+##.
It has eight .
The neutral ##”N”## atom originally had 5 valence electron, and each ##”H”## atom originally had 1 valence electron, for a total of 9 valence electrons.
The positive charge arises because the 8 negative electrons in ##”NH”_4^+## cannot balance the positive charges of the 9 protons in the ##”N”## and ##”H”## nuclei.
Phosphate ion, ##”PO”_4^(3-)##, is a polyatomic anion.
The phosphate ion has 32 valence electrons.
The neutral ##”P”## and ##”O”## atoms originally had only 5 + 4×6 = 29 valence electrons.
The negative charge is caused by the three extra electrons that came from some outside source, e.g., metal atoms that donated their valence electrons and formed cations.