Now this is definitely stumping me. All three are used for "that," pero que es la regla? Gracias.

When does "que" mean "that" Por ejemplo: Yo se que te gusta pan. (I know THAT you like bread) Tu esperas que yo esté hablando con ella (You hope THAT I am speaking with her) In theses examples, "que" is used as "that" to introduce a clause. ESE y ESO are pronouns.

Que can mean "that" when it introduces a clause (as taalibeen points out). However, taalibeen is a little incorrect in claiming that "ese" is a pronoun. ése (with an accent over the first e) is a pronoun meaning "that". If you leave off the accent, ese is an adjective rather than a pronoun. In either case, it means "that," but when it's an adjective, it is used with and modifies a noun. For example, ese carro = that car. As for eso, that's a pronoun meaning "that," but it's used only when you're talking about something abstract that isn't either masculine or feminine. For example, ¿Qué es eso? means "What it that?" Section 4.5 of The Rocket Spanish Beginners Book talks more about all this.