The two verbs are fully different verbs with meanings at least to the Spanish speaker that aren't the same at all. So remember the cardinal rule of translation when you're translating from the English: translate meaning, not words.
The Spanish verb conocer, which comes from the same root as the English words "cognition" and "recognize," generally means "to be familiar with." You would use it in constructions such as these:
- Conozco a Pedro. I know Pedro.
- ¿Conoces a María? Do you know María?
- No conozco Nueva York. I don't know New York, or I haven't been to New York.
- Conócete a ti mismo. Know yourself.
- No sé nada. I don't know anything.
- Él no sabe nadar. He doesn't know how to swim.
- No sé nada de Pedro. I don't have any news about Pedro.
Conocer also can mean "to meet," just as we use might say in English, "pleased to know you" upon meeting someone. Often when conocer is used in the preterite it has this meaning: Conocí a mi esposa en Vancouver, I met my wife in Vancouver. In some contexts it also can mean "to recognize," although there also is a verb, reconocer, that means "to recognize."
And saber can mean "to have flavor," as in sabe bien, it tastes good (estar also is sometimes used in the same way).
Not surprisingly, since both conocer and saber are fairly common verbs, both are irregular, the latter one highly so. Note the accent in sé, the first-person present singular of saber, to distinguish it from se, a reflexive pronoun.
The two verbs also are used in a number of idiomatic phrases. These are among the most common:
- a saber namely
- conocer al dedillo o conocer palmo a palmo to know like the palm of one's hand
- conocer de vista to know by sight
- cuando lo supe when I found out
- dar a conocer to make known
- darse a conocer to make oneself known
- me sabe mal (+ infinitivo) I feel bad about ... (e.g., me sabe mal salir, I feel bad about leaving)
- no saber ni jota (o papa) de algo to not have a clue about something
- no se sabe nobody knows
- para que lo sepas for your information
- que yo sepa as far as I know
- ¿Quién sabe? Who knows?
- se conoce que ... , apparently ...
- según mi leal saber y entender to the best of my knowledge
- ¿Se puede saber ... ? May I ask ... ? (e.g., ¿Se puede saber dónde fuiste? May I ask where you went?)
- se sabe que it is known that
- vete (tú) a saber goodness knows
- ¡Yo que sé! How am I supposed to know?