How would you determine the oxidation number of Sulpher in SO_3^-2?

The oxidation state of sulfur in $S {O}_{3}^{2 -}$ is $+ I V$.
The sum of the oxidation numbers/states of the individual elements in the species must equal the charge on the ion. $O$ normally takes a $- I I$ oxidation state and it does here.
Thus $- 2 = 3 \times \left(- 2\right) + O {N}_{\text{sulfur}}$
And so $O {N}_{\text{sulfur}} = - 2 + 6 = + 4 ,$ i.e. $+ I V$.