How do you know if your 1-601 waiver was approved or denied?

It can take many, many months. They will tell you once they make a decision.

If your case was not screened as immediately approvable, it was sent on to a USCIS office stateside for further review. As my colleague notes, it can take several months for a decision. If the case was submitted to the lockbox, the review is sometimes faster, and notification of the decision is immediate (via email from the Service Center to the Consulate). If the case is being reviwed by another office, you may get aletter notifying you of an approval (or denial), but the Consulate will have to wait for receipt of the actual file from USCIS, which can further delay cases even after they are approved. Waiver applications are complicated and in my opinion, not something that should be on the DIY menu. There's too much at stake and even a minor issues can create unwanted delays and continued separation from family. If you are being asked to provide more information, you should check with an experienced immigration lawyer to see what else may need to be done.

By reading the decision.