How can ohm's law be used to calculate the electrical resistance of a piece of wire?

While you can always use the ratio of voltage to current to determine the resistance of the wire, there is no guarantee that the wire is obeying Ohm's Law! 

This is because Ohm's Law only applies when the ratio of voltage to current is constant for variations in voltage. For example, Ohm's Law doesn't apply to tungsten wire, because its resistance changes markedly for variations in voltage.

There is a general misunderstanding of Ohm's Law that it applies to all materials. This is not true, as it only applies to 'linear' or 'ohmic' materials.

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Newtons laws of motion