I am trying to determine whether or not my sequencing data has more/less non-synonymous mutations than would be expected. My understanding is that there is some fixed ds/dn ratio for the human exome that I can use to calculate this. Is this true? And how might I calculate this?
There isn't a fixed value for the human exome AFAIK, nor would it be a good idea to have a fixed value for the exome because different regions and genes can be under different selective pressures.
The norm is to compute the ds/dn ratio and then test against a null hypothesis of the ratio being 1 to infer if your region is under selection or not. If it is greater than 1 it indicates positive selection and if it is less than 1 purifying selection.
You can find a decent introductory treatment here.