In an ovulation prediction test, urine comes in contact with an indicator, leading to a color change. There is a halachic dispute as to whether this color change creates a problem of tzove’a (dyeing – an activity forbidden on Shabbat). Therefore, you should not perform this test on Shabbat unless there are mitigating circumstances.
When there are mitigating circumstances, such as trying unsuccessfully to conceive for at least six months (or if you are over 35 and have been testing for three months), then you may rely on the lenient opinions and use the test normally.
Note: This answer reflects the position of our current rabbinic supervisor, Rav Kenneth Auman. An earlier version of this question followed the opinion of our founding rabbinic supervisor, Rav Yehuda Henkin.