Already, still, finally
These say where an event stands: done, not yet, ongoing all along, or done after a long wait.
mou
already; (not) anymore
もう
Marks something as done (mou tabeta), or as over for good when the verb is negative (mou ikanai). 'mou ...?' asks whether it has happened yet.
gohan mou tabeta?
Have you eaten yet?
ご飯もう食べた？
gohan wa mou tabemashita ka?
Have you eaten yet?
ご飯はもう食べましたか？
Before an amount, mou means 'more, another': mou ichido (once more), mou sukoshi (a bit more). 'mou!' said alone with a sigh is exasperation, not a time word.
Learn alongside: mada
mada
polite mada desustill; not yet
まだ まだです
Says something hasn't changed yet. mada + negative means 'not yet', mada + -teru means 'still doing', and mada alone answers a 'mou ...?' question.
gohan mada tabetenai.
I haven't eaten yet.
ご飯まだ食べてない。
gohan wa mada tabetemasen.
I haven't eaten yet.
ご飯はまだ食べてません。
'Haven't X yet' is mada + -te nai (mada tabetenai), or just mada (desu). Not mada tabenakatta (= I didn't eat) and not mada tabenai (= I won't eat yet).
Learn alongside: mou
zutto
all along, the whole time
ずっと
Stretches a state or action unbroken across time: zutto matteta (waited the whole time), zutto suki (have always liked).
zutto matteta yo.
I've been waiting the whole time.
ずっと待ってたよ。
zutto mattemashita yo.
I've been waiting the whole time.
ずっと待ってましたよ。
In comparisons it means 'by far' (zutto ii = much better).
yatto
finally, at last
やっと
Shows relief that something long awaited has happened, usually with past tense (yatto owatta).
yatto shigoto owatta.
Work's finally over.
やっと仕事終わった。
yatto shigoto ga owarimashita.
Work's finally over.
やっと仕事が終わりました。
tsuini is the more dramatic 'at last', the climax of a long build-up, and it can mark a bad end (tsuini kowareta = it finally broke). yatto always sounds relieved, and can also mean 'only just' (yatto ma ni atta = only just made it).