They both translate to "to know". The trouble is that French makes a distinction between to ways of knowing something that English doesn't make.
Connaître basically means to know something in the sense of reCOGNizeing it. I capitalized the COGN because they stem from the same Latin word: http://en.wiktionary.org/wiki/conna%C3%AEtre
Savoir is more like "to know [how]" or "to know [that]". So an example where they can both be used but imply different things:
"Je connais l'histoire" = "I know the story"
"Je sais l'histoire" = "I know the story"
The first sentence implies you RECOGNIZE the story, as in you know the story exists. The second implies you know HOW the story goes, as in you are able to retell the story.
My advice, is figure out how to use "Connaître" and if you would not use it, then default to "Savoir"
For more information check out here: http://french.about.com/od/grammar/a/savoirconnaitre.htm
Just looked up the two definitions. "Connaitre" essentially means to have precise, experiential, or competent knowledge of something/one. "Savoir" essentially means informative or instinctual knowledge. http://www.le-dictionnaire.com/definition.php?mot=connaitre http://www.le-dictionnaire.com/definition.php?mot=savoir
I was wondering the same thing. According to LAROUSSE (http://www.larousse.fr/dictionnaires/francais/conna%C3%AEtre/18277?q=connaitre#18172), it's transitive.
To help myself remember the difference, I compare it to "conocer" vs "saber" in Spanish. "Conocer" is like, "are you familiar with this person?" , and "saber" is like knowing a literal answer to a math problem. The C and the S at the beginning of each verb helps me remember the difference in French!
Je connais (I know), tu connais (you know), il connaît (he knows), nous connaissons (we know), vous connaissez (you know, pl), ils connaissent (they know). www.conjugation-fr.com/conjugate.php?verb=connaitre