"Me" vs. "I"

In our most recent COMM 160 session, a fellow student taught us when it is correct to use "I" and when it is correct to use "me."  This problem is most commonly seen in sentences because both "I" and "me" are first-person singular pronouns people use to refer to themselves.  My classmate taught us that "I" is correct to use when it is the subject pronoun used for the person doing the verb. "Me", on the other hand, is the object pronoun used as the object, or receiver, of the action of the verb.  While this definition is very helpful, it is not realistic that a person will be able to think about this mid-sentence and know which word is correct.  Therefore, she taught us a little trick to help us choose the correct word.  When confronted with the problem of "I" vs. "me", simply take out the other person in the sentence and see which word would be correct.  For example, if the sentence were "He sang to Jill and (me/I)", it would be correct to say "He sang to Jill and me." If you took out Jill, the sentence would then read, "He sang to me" which would be correct, not "He sang to I."