If the pronoun is acting as a subject, use who. If it is acting as an object, use whom.

I don't know whom Kate married.

Why is whom correct? Because Kate is the subject of this sentence – not the person she married. To simplify who/whom questions, try rearranging the sentence into a question, and then answer it. Let's try it:

Question: Who/m did Kate marry?
Answer: Kate married him.

You wouldn't say "Kate married he," right? Since the pronoun used in the answer is "him," an object pronoun, the pronoun in the original sentence should also be an object pronoun: whom.

Here's another one to try:

Who took out the trash?

Because the sentence is already a question, you can't run the test as we did above. But not to worry: all you need to do is answer the question:

He took out the trash.

You wouldn't say "him took out the trash," so the pronoun in the original sentence must match the form of the pronoun "he," which is a subject pronoun: who is correct.

B. Subject vs. Object

D. Singular and Plural Pronouns