まだ

まだ means "still" in an affirmative sentence and "not yet" in a negative one. It goes before the part of the sentence it describes, usually near the front.

"Not yet" takes 〜ていない

Something that hasn't happened yet takes the 〜ていない form of the verb, or 〜ていません in polite speech: the state of not having done it carries on into now. The past negative is the form English pulls you towards, and it says the chance is over.

• × まだ食べませんでした → まだ食べていません

A plain negative after まだ is about what you are going to do: "not yet" as a decision.

まだ and もう

もう is "already". A question with もう gets まだ as its "not yet" answer, on its own or as まだです.

With a negative, もう means "no longer", so the two face opposite ways: まだ says the thing is still there, もう that it has gone.

まだまだ

Doubled, まだ means there is still a long way to go. まだまだです is also the modest reply to a compliment.