Still means that something is continuing and hasn’t stopped or changed.  It is often used with a verb and in the middle of a sentence.  
Yet  means “until now.”  It is often used in negative sentences and usually goes at the end of the sentence.  
Already is used to say that something happened earlier than it should have and is usually used in the middle of the sentence.

 Here are some similar sentences with each word to help understand how to use them:

     “I still haven’t finished reading that book you lent me.” = this means that you started reading the book and are still doing it and haven’t stopped
     “I haven’t finished that book you lent me yet.” = this means that maybe you and/or the person that lent you the book assumed or thought you’d be finished reading it by now, but you haven’t
     “I already finished that book you lent me.  I’ll return it to you tomorrow.” = this means that you finished the book before now and it was earlier than either you and/or the other person expected

Here are some more examples:

    “We are still working on that project and hope to finish it soon.” = this means that the project is still in process and is not finished
    “We haven’t finished that project yet, but we hope to finish it soon.” = this means that the project isn’t finished as of right now
    “We already finished that project yesterday.” = this means that the project has been finished and maybe earlier than expected
    “She is still trying to learn enough French to get a job in France.” = this means that she is continuing to learn French and it is still in process
    “She hasn’t learned enough French to get a job in France yet.” = this means that she is trying to learn French but hasn’t managed to learn enough for what she needs
    “She has already learned enough French to get a job in France.” = this means that she has finished the process of learning enough French to get a job
    “Sandra is still trying to decide which house to buy.” = this means that Sandra is in the process of deciding which house she wants to buy