How are positive and negative ions formed

An ion is formed when a neutral atom gains or loses an electron.

A neutral atom has the same number of protons (+) and electrons (-).

If it gains another electron, it has too many negative charges, so it's a negative ion.

If it loses an electron, it has too many positive charges, so it's a positive ion.

What if it gains or loses a proton ?

That's a great question.  I'm glad you asked.

Under normal circumstances, this hardly ever happens.  But if it did ...

- If it somehow lost a proton from its nucleus, first of all, it would change the number of protons in the nucleus, so the atom would immediately become an atom of a different element.

- If it didn't lose an electron at the same time, then it would have too many electrons for the number of protons in the nucleus, so it would be a negative ion of the new element.

-  If it somehow added a proton to its nucleus, it would change the number of protons in the nucleus, so the atom would  become an atom of a different element.  If it didn't add another  electron at the same time, then it would have too few electrons for the number of protons in the nucleus, so it would be a  positive ion of the new element.