the question is interesting. WHY has an ion a charge... The simple answer to that is that the ionic form is more stable than the neutral NO
3 would be.
More elaborate: it can be shown from the Molecular Orbital diagram where can be shown that 24 electrons would fill all bonding s and pi orbitals without having any in the antibinding ones. NO
3 has 23 electrons (6 per O and 5 for the N), so the -1 form with 24 electrons is the more stable one (this also shows that -2 is not favored as it would have an electron in an antibinding orbital)
in the
MO sketch the extra electron is shown in red. It is the last one to fill up the pi bonding orbitals
PS. this might be much more advanced than you want it to be. But in any case the best way to go about these ions and their charges is just to memorize what ion has what charge.