Lemme see, how can I explain this? First of all, which is the default? Sapere. In the very common phrases such as "I know" or "she doesn't know," sapere is used. Also in any phrase of the type "do you know where/how/why/when/what...?" It is also in the expression "that I know of," which is translated as che io sappia (notice the subjunctive- isn't Italian fun?). A very large area is covered by things you learned such as skills and aquired knowledge: I can play the piano, tennis; I can knit, make gnocchi; I know French, integral calculus, what the capital of Vermont is. Just for the hell of it, Italians will sometimes use conoscere in some of these phrases: Mi dispiace, non conosco l'inglese- "sorry, I don't know English."
The famous admonition at Delphi, Gnothi seauton (know thyself) is conosci te stesso. Socrates' unheard of profession of ignorance (for a male) oida hoti ouk oida (I know that I don't know) is so di non sapere. I bet ole Socrates even asked for directions: scusi, saprebbe dirmi come si arriva all'agora' ?- excuse me, do you know how to get to the agora?
That leaves us with conoscere. It's useful to think of this more in terms of recognition (notice the common Latin root.) Ask yourself: have I been exposed to this, would I recognize it? All uses of knowing somebody use this term: Non conosco sua moglie- "I don't know his wife". The idea of familiarity, also similar to the concept of recognition, takes conoscere: conosco bene Venezia, "I know Venice well."
My grand theory: conoscere seems to imply exposure to someone or something (even extensive), sapere naturally includes exposure but also understanding and depth, a learning process. Like all grand theories, it has its limits. But that's the Italians' fault, not mine.
Let's take a little test to see if you can use these properly. The key at the end will have the letters s or c for the two words.
Would you use sapere or conoscere in the following?
1. I don't know where your damn keys are.
2. He doesn't know her brother.
3. I know what you're thinking.
4. She didn't know they were coming.
5. I don't know what to do.
6. He doesn't know who Michael Schumacher is.
7. He doesn't know Michael Schumacher.
8. I know, I know.
9. Who the hell knows?
10. Do you know each other?
11. He doesn't know how to get to Siena, but he won't ask.
12. The motives for the crime are not known.
13. I don't know the answer.
14. I know you like the back of my hand.
15. She doesn't know his address.
16. Do you know the difference between sapere and conoscere?
17. Forgive them Father for they know not what they do.
18. You don't know what you're saying.
(Don't peek!)
1. s 2. c. 3. s 4 .s 5. s 6. s 7. c. 8. s 9. s. 10. c. 11. s 12. c 13. s or c 14. c 15. s (c possible but less likely) 16. s 17. s 18. s