All three words can be used to talk about actions or situations that are going on or expected around the present.
Still is used to talk about situations that are still not finished.
- It is still raining.
- Is she still working?
- I have been waiting for hours, but I still haven’t heard anything from them.
- You are still seeing him, right?
Not yet is used to say that something which is expected to happen is in the future – it hasn’t happened yet.
- She has not yet arrived.
- I have not yet received that letter.
In questions yet can be used to ask whether an expected activity has happened or not.
- Has the postman come yet?
- Are you ready yet?
Occasionally yet is used in affirmative sentences with a similar meaning to still.
- We have yet to hear from them. (= We are still waiting to hear from them.)
Already is used to talk about a situation that has already happened.
- The visitors have already arrived.
- We have already finished.
- ‘You must go to Venice.’ ‘I have already been.’
In British English, perfect tenses are common with already and yet. Americans often use past tenses with these words.
- Have you called them yet? (GB)
- Did you call them yet? (US)
- She has already arrived. (GB)
- She already arrived. (US)