Still or Yet?

Still is used to say that something is in the present, not the past - it has, perhaps surprisingly, not finished.

She's still asleep.

I've been thinking for hours, but I still can't decide.

Not yet is used to say that something which is expected is in the future, not the present or past.

The postman hasn't come yet.

Has the postman come yet?

Yet is normally used in questions and negative sentences, but it is occasionally used in affirmative sentences (with a similar meaning to still) in a formal style.

We have yet to hear from the bank. (=We are still waiting to hear...)

Swan, Michael. 2002. Practical English Usage. Oxford: OUP.