This is quite a complicated one and, indeed, most reference sources do state that “who” is used most of the time now, and that that can be seen as being correct. In other words, “whom” is dying out. And it’s a slightly nerve-wracking one to do, as people get in such a fuss about it.
But I think I’ve found a way to differentiate quickly between the two, so here goes …
Who is used when referring to the subject of the sentence (the person who is doing, we might say), and whom to the object (the person who is being done to).
So – “The person who is going to the ball”; “The person who is speaking to me”, but “The person whom I am taking to the ball”, “The person to whom I am speaking”
I hope I’ve got that the right way round!
For more troublesome pairs, choose the phrase in the category cloud to the right, or click here.