Already, still or yet?
from English Grammar Today
 
Already or yet?
We use already to refer to something which has happened or may have happened before the moment of speaking. Already can sometimes suggest surprise on the part of the speaker, that something is unexpected:
Is it seven o’clock already? (The speaker didn’t expect it to be so late.)
We use yet most commonly in questions and negatives, to talk about things which are expected but which have not happened:
Is it seven o’clock yet? (The speaker thinks that probably it’s almost seven o’clock.)
A:
Where will you be staying?
B:
I haven’t decided yet, but somewhere in the city centre.
Already refers to things which have happened or which people think may have happened. Yet refers to things which have not happened or which people think may not have happened.
 
Already, yet or still?
We use still not yet or already to refer to the continuation of a situation:
I still meet my friends from my schooldays now and then. (I continue to meet my friends)
Not: I already meet my friends or I yet meet my friends
Compare

A:
Is your sister still at university?
B:
Yes. She’s got one more year to do.
I know she was at university. Does that continue to be true?
A:
Is your sister at university yet?
B:
No. She’s only 17. She’ll go next year.
I expect that she will go to university. Is she there now?
A:
Is your sister already at university? She’s only 17!
B:
Yes. She started this year. She’s so clever they let her enter a year early.
I’m surprised if your sister is at university. I did not expect it to happen until later.
 
Negatives with already, still, yet
Negatives with yet mean that something has not happened up to now:
I haven’t spoken to Henry about the car yet.
Negatives with still suggest that the situation should have changed, but it has not:
I still haven’t found my passport. I know it’s here somewhere. (I’ve been looking for it for a long time. I should have found it by now)
Warning:
We usually put yet after the main verb, whereas we usually put still after the subject.
Compare

I haven’t finished yet.
I still haven’t finished.
You know, it’s dark now and she hasn’t arrived yet.
You know, it’s dark now and she still hasn’t arrived.
Negatives with already are far less common than negatives with yet and still. They usually refer to things which should have happened before they did happen:
If you’ve already registered, the price is 50 pounds. If you haven’t already registered, it’s 75 pounds for late registration.
I was surprised that they hadn’t already told me the news.
See also:
Already
Still
Yet