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.