Both verbs can be translated as to know, but they have different meanings.
Use conocer when you mean "being familiar" or "being acquainted" with a thing, a place or a person.
I know Juan. (Meaning I’m acquainted with Juan).
Conozco a Juan. (We have to use the personal a).
I know the rules. (Meaning I’m acquainted with the rules).
Conozco las reglas.
Use saber for skills (as in how to do something)
I don’t know how to swim. (Meaning I can’t swim).
No sé nadar.
I know how to play the piano. (Meaning I can play the piano.)
Yo sé tocar el piano.
Use saber for “information:”
I know that Peter lives in Viena.
Sé que Peter vive en Viena.
I know that you don’t know her.
Yo sé que tú no la conoces.
An easier way of looking at them
If you read the examples above, you’ll notice some structural differences: conocer usually takes a thing/place/person as a direct object (conozco [algo/a alguien]), while saber usually takes either verbs, for skills (nadar, tocar el piano) or subordinate clauses connected by que, which have a subject and a verb ([que] Peter vive en Viena, [que] tú no la conoces), for “information.”