Lesson 33: Still, already, and yet with もう まだ 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".
もうそんな時間ね That kind of time already, huh?
もう食べた I already ate.
もう食べない I won't eat anymore.
もういいよ Metaphorically: "It's good already."
もう！ Metaphorically: "Enough!"
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.
Another use of もう expresses "more" of an amount. This has a different accent but it's usually considered the same word.
もう一回！ One more time!
もうちょっと A bit more
まだ expresses the idea of "still" or "yet" as in the opposite of もう. It's used when a state stays the same.
まだ来た
まだ食べるの？ You still eating?
まだ負けないな！ I'm not beaten yet!
まだまだ "Not yet!"
もう is used for "yet" in positive questions, since もう concerns a change, and まだ concerns staying the same. もう can still mean "already" in questions, though.
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". Try not to confuse this with まだ.
また来た He came again.
また来ないな Looks like he's not coming, again.
また来なかった Didn't come again.
The last three examples are slightly ambiguous, both in japanese and english.