The first thing to say is that there is no one-to-one correspondence between the tense/aspect/mood of Spanish and English verbs.
Whereas English has only one simple past, Spanish has two: pretérito simple and pretérito imperfecto.
In general, one can translate both the pretérito simple and pretérito imperfecto into simple past. In many cases the context is enough to ensure no information is lost in the translation.
However, when translating the English simple past into Spanish, one has to decide which choice, pretérito simple or pretérito imperfecto, is more appropriate.
The criterium for this choice is what it is called in grammar the perfect aspect as I will explain next.
Both the pretérito simple and the pretérito imperfecto are past tenses, and hence, they describe actions that took place in the past. However, whereas:
the pretérito imperfecto (sabía, sabías, sabía...) has not perfect aspect,
the pretérito simple (supe, supiste, supo...) has perfect aspect and this means the action described by the verb not only took place in the past, but also happened before another event in the past. Hence, it is not appropriate to use pretérito simple unless the context provides this additional reference in the past.
OK, the explanation above is pretty abstract, let's borrow Zane's example to see how it works:
I did not know that school started at 9:00am today.
In principle, there would be two possible translations:
No sabía que la escuela empezaba hoy a las 9:00 (pretérito imperfecto)
Without additional context, I believe the pretérito imperfecto is the most appropriate translation. It simply states that, at some point in the past, you didn't know something.
Without additional context, the use of pretérito simple sounds incorrect:
No supe que la escuela empezaba hoy a las 9:00 (pretérito simple)
However, if the sentence is completed with additional context defining another event in the past, then the use of pretérito simple becomes the most appropriate choice:
No supe que la escuela empezaba hoy a las 9:00 hasta que tú me lo dijiste (pretérito simple)
Note that "tú me lo dijiste" is also pretérito simple, but explaining this choice of tense deserves another question.