Ions are not neutral, they are by definition charged particles. Ions form when atoms gain or lose electrons. Since electrons are negatively charged, the loss of an electron results in a positive ion. As an example, sodium loses one electron to form Na+ and calcium loses two electrons to form Ca2+. These are positive ions because they now have more protons than neutrons, while neutral atoms contain an equal number of protons and electrons and therefore have a net charge of zero. (Protons are positively charged particles.) Negative ions form when an atom gains electrons, such as chlorine gaining one electron to form Cl- and oxygen gaining two electrons to form O2-. Note that atoms do not gain or lose protons, which are in the nucleus, only electrons, which are outside the nucleus.
Polyatomic ions are groups of atoms that have a net charge, such as the nitrate ion, NO3-, which consists of one nitrogen atom atom, three oxygen atoms and an extra electron.