Still, already, and yet with もう, まだ, and また

With positive statements, もう expresses "already". With negative statements, it works together with the negation to express "not anymore".

Basically, もう means that there's a change of state from the statement being false or irrelevant to the statement being true: "already" and "not anymore".

もうこんな時間だ
It’s this late! (lit. It’s already this time)

もう食べたよ
I already ate

もう食べないの？
You won’t eat anymore?

もう can also appear as an emphatic expression of frustration

もういいよ
I’ve had enough (lit. it’s already at a sufficient level)

もう！
(angry frustrated noises)

In statements about the near future, もう can mean "soon" instead. This usually goes along with an adverb expressing soonness, but sometimes it's just implied.

どうやらもう来るみたい
Well it seems like he’ll arrive soon

Another use of もう expresses "more" of an amount.

もう一杯！
One more drink!

もうちょっと
A bit more

まだ expresses the idea of "still" or "yet" and it is the opposite of もう. It's used when a state stays the same.

まだ食べるの？
Are you still eating?

まだ負けないな！
I haven’t lost yet!

まだまだ
Not yet!

まだまだ is an adverb and set expression that also works as a more emphatic まだ

もう is used for "yet" in positive questions, since もう highlights a change.

もう書きましたか？
Did you write it yet?

もう眠いの？
Are you already sleepy?

また expresses the idea of "again".

また来た
He came again.

また来ないな
Looks like he's not coming again.