Still refers to an action that began in the past and is continuing in the present.
Still is used in positive, negative and question forms.
Still is usually either after the subject or after the verb.
Mary is still looking for a job.
I still haven’t finished the project.
Are you still there?
Yet refers to an action which is presumed to happen, but hasn’t happened until now.
Yet is used in negative and question forms.
Yet is always at the end of the sentence.
I haven’t told anyone else yet.
Have you talked to your boss yet?