もう〜ました・まだ〜
Already … / still, not yetmachine translation
Formationもう + ました form / まだ + affirmative sentence (or まだです)
もう + the ました form means "already did …": もう食べました — I've already eaten. The question もう〜ましたか asks whether something is done yet.
When answering "not yet", don't say いいえ、食べませんでした (it sounds like "I didn't eat that day") — say まだです or まだ食べていません: "I haven't eaten yet".
まだ + an affirmative sentence means "still": まだ時間があります — there is still time.
Examples
もう昼ご飯を食べましたか。
Have you eaten lunch yet?
手紙はもう書きました。
As for the letter, I've already written it.
まだ時間がありますよ。
There's still time, you know.