Many people have trouble with deciding when to use "who" and when to use "whom." Simple answer: "Whom" is always wrong. But if you want to go beyond the simple answer, there is a fairly easy way to know when to use which.
The technical explanation is that "who" is used in the subject position of a clause, while "whom" is used in the objective position: Who kicked whom. If you're not sure which one to use in a given situation, try this: Substitute the word "who" or "whom" with the word "he" or "they." For example, if I write,
"I am looking for the person ___ molested the hippopotamus"
I could place the word "he" in the blank: "He molested the hippopotamus." That sounds grammatically correct (if morally unacceptable). Thus, the correct word to use in that clause would be "who." But try this:
"I am looking for the person ___ the hippopotamus molested"
Well, if I say, "He the hippopotamus molested," that sounds weird. I could say, "The hippopotamus molested he," but that sounds even worse. On the other hand, "The hippopotamus molested him" sounds juuuuust right--if kind of horrifying. In this case, then, the correct word to fill in the blank would be "whom."
Briefly, then, the rule is, "If he/they would fit in the sentence, the correct relative pronoun is 'who'; if him/them would fit, the correct relative pronoun would be 'whom.'
Now, admittedly, this is not the most crucial rule in the ol' grammar database. Many people could happily go through their entire lives using "who" or "whom" interchangeably, or never using "whom" at all. Still, the knowledge comes in handy, especially if one is--oh, I don't know--FILLING OUT AN APPLICATION FOR A FULL-TIME POSITION AS AN ENGLISH PROFESSOR!!!