Already is the opposite of yet. They both have the sense of before now, but already has a feeling of being early, whereas yet has a feeling of something being late. It can be in the middle or the end of a sentence.
She has already learned how to dance.
We just bought that car, but it's already worn out.
They've suffered enough already.
Still is a continuation of a situation, used with any tense and is positive or negative. It is in the middle of the sentence.
She is still learning how to dance.
Our car is old, but it still runs well.
We still haven't figured it out.
Anymore is the opposite of still and has the idea that something has been discontinued. It's used with a negative word (not, never). It comes at the end of the sentence. It's the same as no longer.
She doesn't dance anymore. / She no longer dances.
Our car is so old that it doesn't run anymore. / It no longerruns.