French has two verbs which can be translated by the English verb "to know": savoir and connaître. This can be confusing to English speakers, but in fact there are distinct differences in meaning and usage for the two verbs.
Savoir has three possible meanings:
1) to know a fact
Je sais qu'il l'a fait.
I know he did it.
2) to know by heart
Je sais cette nouvelle (par cœur).
I know this short story (by heart).
3) to know how to do something (note that the word "how" is not translated into French)
Savez-vous conduire ?
Do you know how to drive?
Je ne sais pas nager.
I don't know how to swim.
In the passé composé, savoir means "to learn" or "to find out":
J'ai su qu'il l'a fait.
I found out that he did it.
Savoir is often followed by a subordinate clause.
Je sais où il est.
I know where he is.
Il sait que nous serons à la fête.
He knows we'll be at the party.
Connaître has two meanings:
1) to know a person
Je connais Pierrette.
I know Pierrette.
2) to be familiar with a person or thing
Je connais bien Toulouse.
I know / am familiar with Toulouse.
Je connais cette nouvelle - je l'ai lue l'année dernière.
I know / am familiar with this short story - I read it last year.
In the passé composé, connaître means "to meet (for the first time) / become acquainted with":
J'ai connu Pierrette à Lyon.
I met Pierrette in Lyon.
Connaître always needs a direct object:
Je connais son poème.
I am familiar with his poem.
Je connais bien ton père.
I know your father well.
Nous connaissons Paris.
We know/are familiar with Paris.
Il la connaît.
He knows her.
Ignorer is a related verb which means "not to know" in the sense of "to be unaware of." Depending on the context, it can replace either ne pas savoir or ne pas connaître.
J'ignore quand il arrivera.
I don't know when he is arriving.
Il ignore Ionesco.
He's not aware of (doesn't know about) Ionesco.
Now that you know how to know, take the test on savoir vs connaître.