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First you should look at the overall charge. From there you should identify components of the compound where you know what charge it is. For example you know that elements in group 1 and 2 would have a charge of +1 nad +2 respectively, and elements in group 16 and 17 would have -2 and -1. Then look at how many atoms of the elements with the charge you know there are and calculate what the unknown charge of the remaining element would be corresponding to the overall charge.
Since in coordination compounds, atoms are basically surrounding the metal ion, so to find the oxidation state of the metal ion, you'll have to look at the charges of the ligands, the coordination compound's overall charge, and atoms bonded to the compound (if any). For example, in [NiCl2(NH3)4]2H2O the cl- ions have a -1 charge each, the NH3 molecules have no charge, the overall coordination compound has no charge, and the H2O molecules have no charge. The overall negative charge of the ligands and molecules is -2 because of the 2 cl- ions. Thus, the Ni cation has to have a 2+ to balance it out.
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