To Know and To Know.
I know there are two different ways to say " To Know" but how do you know which one you use?
2 Answers
Saber is to know factual information: ¿Sabes a qué hora cierra la biblioteca? Do you know what time the library closes?
Think of conocer as meaning to be familiar with a person or place. ¿Conoces Madrid? Do you know [are you familiar with] Madrid? Conozco a su amiga. I know her friend.
Conocer in the preterite means to meet for the first time. ¿Conoces a mi mamá? Sí, la conocí ayer. Do you know my mom? Yes, I met her yesterday.
It may (or may not) help to remember that "conocer" shares its origin with "reconocer (recognize, in English). We also have the word "cognizant" in English (from the same Latin root) but it is not used all that much, these days. In any event, the sense is "to be familiar with" / "to recognize" / "to be acquainted with".
Neither English speakers (nor Spanish/French) speakers would ask "Do you recognize how much 2+2 equals?" The "knowing" is not one of "recognizing" or "familiarity" but of "understanding". This distinction can be traced back at least as far as Plato's writings (that which is simply the product of experience and that which transcends mere experience).