When an atom gives up or takes on an electron, the positive and negative charges are no longer balanced. Extra electrons give an ion a negative charge. Fewer electrons give an ion a positive charge. Adding neutrons to atoms does not affect charge, but it will affect atomic mass. This is why atomic mass is not reported as a whole number on the periodic table.
Elements exist as a group of different isotopes.
A neutron, like a proton, contributes one atomic mass unit to the total atomic weight of an atom. The table puts elements into groups with similar characteristics, allowing us to recognize trends over the whole array of elements. A proton contributes one atomic mass unit to the total atomic weight of an atom.