How do antidepressants cause secondary amenorrhea?

Depends. All antidepressants have hormonal effects, but would need to know specific antidepressant to give you any additional details.
Good question. We don't know exactly how antidepressants cause amenorrhea but sometimes it can be due to high prolactin elevation which some antidepressant agents can cause. Check with your physician/endocrinologist if further work is needed. Of couse, it goes without saying that a pregnancy test is needed in any women with secondary amenorrhea.