Both already and yet are used for talking about changes, actions, or states that happened or existed before the present time or before a particular time that you are referring to.
Use already in positive sentences or in questions when you think it is likely that something has happened or existed before, or when you know it has happened or existed before and are surprised: Thanks, but I’ve already eaten. ♦ Did I already give you my e-mail address? ♦ Is John married already? He hardly looks old enough.
Use yet in negative sentences and in questions, especially when you think that the change, action, or state should happen or exist soon: Kim hasn’t seen the movie yet, so don’t tell her how it ends. ♦ Have you told her yet that you’re leaving? ♦ Aren’t they here yet? It’s after 8:00.
Use still for talking about actions, conditions, or states that continue happening or existing without changing: Are you still working downtown? ♦ I’d still like to talk to you when you get a chance. ♦ He had eaten three hamburgers, but he still wasn’t full. You can also use still for expressing surprise that a situation has not changed: ♦ You’re still here? I thought you left hours ago.