First of all, it is pronounced "chee." To examine its use in Italian, let's break it down into its various functions. Or at least let's try. I have yet to find a satisfactory treatment in a grammar. That's how idiomatic the little critter is.
As a form of "there":
Ci sono molti laghi in America.
There are many lakes in America.
C'e' Marco?
Is Marco there?
Non c'erano piu' quando siamo arrivati.
They were no longer there when we arrived.
Vacci tu.
You go (there).
As a form of "here":
Viviamo in Francia. Ci siamo da tre anni.
We live in France. We've been here three years.
Mi dispiace, non c'e'.
Sorry, he's not here.
As the direct or indirect object of noi:
Dacci oggi il nostro pane quotidiano.
Give us this day our daily bread.
Ci ha detto di stare zitti.
He told us to shut up.
Papa' ci vuole molto bene.
Dad loves us very much.
Non ci piace.
We don't like him/her/it. (literally: he/she/it does not please us)
Ci piacciono molto.
We like them a lot. (literally: they please us very much)
To express reciprocity when the speaker is included ("each other"):
Ci odiamo.
We hate each other.
Ci vediamo!/ci sentiamo!
See you!/talk to you soon! (literally: we'll see each other/we'll hear each other)
Arrivederci!
Good-bye! (a rivederci- till we see each other again)
Nella mia famiglia non ci facciamo mai regali.
In our family we never give each other presents.
As a reflexive particle when the speaker is included ("ourselves"). Sometimes the reflexive is not expressed in English.
Ci guardiamo allo specchio.
We're looking at ourselves in the mirror.
Ci siamo svegliati alle otto.
We got up at eight. (literally: we woke ourselves at eight)
Siamo in ritardo perche' ci siamo persi.
We're late because we got lost. (literally: we lost ourselves)
As an idiomatic form of "it" (often impersonal "it"):
Ci vogliono quattro ore da Boston a New York.
It takes four hours from Boston to New York.
Non ci credo.
I don't believe it.
Ci penso io.
I'll take care of it. (literally: I'll think of it)
Ci ho/c'ho (informal) messo due uova e un po' di vaniglia.
I put two eggs and a little vanilla in it.
C'ho messo tre ore a scrivere quella lettera.
It took me three hours to write that letter.
Other uses (unexpressed in English):
Ci vedi?
Can you see? (it can also mean "can you see us?")
Che c'entra?
What does that have to do with it?
Non ci voglio piu' stare con Enrico.
I don't want to stay with Enrico anymore.
Non ci sto!
I don't agree/don't accept this/am not going to put up with this.
Are you having fun yet? No?
OK. When our little critter is followed by the object pronouns lo, la, li, le or ne (another terrible little word), it changes into ce. That way you can confuse it with c'e' and make an even bigger mess of things.
Ce lo dai?
Will you give it to us?
Non ce ne sono piu'.
There aren't any more.
Aiuto! Non ce la faccio piu'! Non ci capisco piu' niente! Non c'e' nessuno che ci possa aiutare con questo ci?
Help! I can't take it anymore! I don't understand a damn thing! Isn't there anyone who can help us with this ci?
Exercises will follow later in the week. Ci potete scommettere (you can bet on it.)
