Let's consider the simple case of ammonia, NH_3, versus its ammonium salt, NH_4^+. Now ammonia is a neutral molecule, and there is a non-bonding pair, a lone pair, of electrons localized to the nitrogen centre. Its reaction with H^+ is very simply represented:
NH_3 + H^+ rarr NH_4^+
The ammonium is now quaternized. Why? Well, any chemical reaction conserves mass and charge, and this one does as well. But why do we write ammonium as NH_4^+, with a formal positive charge on the nitrogen nucleus?
The nitrogen in ammonia, NH_3 is neutral because it shares 3 electrons from the 6 electrons that comprise the N-H bonds, and gets a full contribution from its lone pair, i.e. 5 electrons + 2 inner electrons electrostatically balance the 7 protons in the nucleus of a nitrogen atom. When N is quaternized as ammonium, NH_4^+, it is conceived to have a 1/2 share only of the 8 electrons of the N-H bonds, 4 e in total, and is therefore written as NH_4^+, with the positive charge formally associated with the nitrogen atom.