How is the charge of an atom determined?
how is the amount of neutrons determined?

Atoms have positively charged protons and negatively charged electrons, the number of each tells you the charge.
The ionic charge is the number of protons subtracted by the number of electrons. They usually have the same charge, but with opposite signs, Electrons ( -) and protons ( +)
 To find the neutron number,subtract the proton number from the atomic mass. It will give you the neutron number.
Hope this helps.
 

Yes you are correct use the scientific method