Still is used to say that something in the present hasn’t finished.
- I am still on the toilet.
- You have had six sandwiches. You can’t still be hungry.
Yet is used to say that something hasn’t happened. It only talks about the present situation and cannot be used for the past nor the future.
- I haven’t spoken with him yet.
- I haven’t visited the Tate Gallery yet.
Already is used to talk about something that happened sooner than expected.
- I have already done my homework.
- It is already one year since she left me.