In regular spoken English, simply use "who" unless following a preposition.

"To whom did I give the painting?"
(alt): "Whom did I give the painting to?"
"Who recieved the painting?"

The general rule is: "who" uses the subjective form (like "he", "she" or "they"), "whom" uses the direct or indirect object form (like "him", "her" or "them"). If someone is performing action, use "who":

"He kicked me." "Who did he kick?" "Me."
"I think she is dead." "Who do you think is dead?" "She is."

The last example shows that you must think back to the original sentence structure to choose the correct word. Instead of saying "She is," we could just have easily said "Her."

"I gave herpes to a Thai prostitute." "Whom did you give herpes to?" "Her."
"I was speaking to her." "Whom were you speaking with?"

Getting this right takes practice -- it will sound incorrect for the first few months until a general feel is established. During this time, expect to be the butt of obnoxious assholes who will not understand that proper English is a sign of intelligence, much like taking a bath or not spitting on sidewalks. Just be sure you've got it right before you open you mouth, lest you be deemed an idiot for answering the door "Whom is it?"