もう + [verb た-form] もう + [verb ない-form] もう + [number + counter] もうすぐ
"Already" goes with something that is done, so the verb is usually in the past. In a question it is English "yet".
It also goes with です, for a time or a state that has been reached.
With a negative, something that used to be true has stopped.
In the past, a negative with もう says that someone stopped: "did not … any more".
The opposite of もう is まだ. When the answer to a もう question is no, it is まだです, or まだ with ~ていません. A negative past does not say "not yet": in reply to もう食べましたか, ×いいえ、もう食べませんでした means "I didn't eat any more", not "not yet", and ×まだ食べませんでした is wrong as a reply.
Side by side:
These go beyond "already" and "not any more".
In front of a number or an amount, もう means "more" or "another". It comes before the number: ×一度もう is wrong.
On its own, or at the front of a complaint, もう shows the speaker has run out of patience. It belongs to casual speech.