If an atom gains an electron, what is its charge?

If an atom gains am electron it's charge is negative.

Almost right! Electrons are negatively charged so they will make an atom more negative. What the atom's charge becomes depends on what it was to begin with.

For example is a Magnesium ion Mg+2 gains one electron it is still positive Mg+1 as the electron was not enough on its own to make it negative.