You look at your test statistic and if it was created by taking the ratio of two independent Chisquare random variables divided by their degrees of freedom then the numerator degrees of freedom is equivalent to the degrees of freedom of the chi-square in the numerator of the ratio. The denominator degrees of freedom end up being the degrees of freedom of the chi-square in the denominator.

If the F-stat arose some other way (I can't think of any off the top of my head) then you'll have to figure it out some other way.

Or you could just do what jrai mentions because that's probably what you're looking at?