It's actually not that easy sometimes; in fact, some would like nothing more than to rid the word from our language.

The rule I go by is:
"Who" corresponds with "he" (subject)
"Whom" corresponds with "him" (object)

So a quick word replacement is one way to determine which to use... most of the time.

"He gave the book to him?"
"Who gave the book to him?"
"He gave the book to whom?"

I'm sure I get it wrong sometimes, though. That link has some complex examples I'd've gotten wrong. And some people think it's pretentious - the same people who cannot use "we"/"us" and "I"/"me" properly...