Statistics: How to determine correlations between nominal variables?

Tl;dr: I’ve got two non-linear (nominal) variables here, and I need to figure out whether there’s a statistically significant correlation between the two.

Long version: As part of my thesis, I’ve been looking at a heckload of different languages and determining for each language how they handle two constructions, in order to figure out if there’s a connection between particular approaches. The hypothesis in a nutshell is that if a language uses approach X for construction A, it’ll use approach Y for construction B.
And now I need to figure out whether the data support the hypothesis or not. And I’m not sure how to do that.

Can you point me in the right direction?

I fail at statistics. :/