Rule of thumb:
Savoir is used to express information that has been acquired.
---For example: Je sais que Paris est la capital of France. (I know that France is the capital of France).
Connaître is used to express familiarity. It is used with people and places. For example: Je connais Paris. (I know Paris.) = I have been to Paris and am familiar with the city.
Let's take another example:
- Je connais Robert. (I know Robert.) = familiarity
- Je sais que Robert est le frère de Véronique. (I know that Robert is Veronique's brother.) = a fact that you acquired or learned along the way
***Helpful hint: connaître is always followed by a noun. [connaître + noun]
Savoir can also be used to express "to know how". For this connotation, it will be followed by the infinitive (non-conjugated verb)
- Je sais nager. = I know how to swim.
- Je sais parler français. = I know how to speak French
**Note that the "how" is not included in the French sentence
And if you just want to say, "I know", you'll always use savoir: Je sais!