What it means
もう is an adverb meaning “already” with an affirmative predicate and “no longer” with a negative predicate. It usually appears before the predicate. With an affirmative past verb, it shows that an action has been completed. With a negative verb, it shows that an action or situation has stopped or will not continue. もう does not itself make a sentence familiar or polite; the predicate determines the register.
Usage note
With a negative predicate, もう usually means “no longer,” while まだ～ない means “not yet.” Do not confuse these two patterns.
How to use it
私はもう昼ご飯を食べました。
I already ate lunch.
私はもうこの薬を飲みません。
I no longer take this medicine.
私はもう昼ご飯を食べた。
I already ate lunch.
私はもうこの薬を飲まない。
I no longer take this medicine.
Example sentences
妹はもう宿題を終えました。
My younger sister has already finished her homework.
父はもう昼ご飯を食べました。
My father has already eaten lunch.
図書館はもう閉まりました。
The library has already closed.
私はもう新しい自転車を買いました。
I have already bought a new bicycle.