Still? Enough Already!

In this Topic, we're going to learn how to say that something 'already is' and 'still is'. To do this, we will use the adverbs もう and まだ. For this pair of words, special attention needs to be paid to how tense and ている interact with them to create natural sentences.

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もう
Already, Anymore
In English, もう is regularly translated to 'already', or 'anymore', depending on if it is used in a positive-past (already), or negative (anymore) sentence. The reason that Japanese only requires one word for both of these nuances is due to もう literally meaning 'something has unexpectedly ended'.
From these sentences we can see that もう can be translated in each case as the following.

(Past) - Although expected to not be done, it is. 'Already', in English.

(Negative) - Although expected to still be going, it isn't. 'Anymore', in English.

This is the opposite of まだ, which means 'something is unexpectedly still going'.

もう may also be used to ask questions. This is when the speaker thinks that something 'might' have ended, but wants to confirm.
Fun Fact

もう is often used simply as an expression of exasperation (giving up on arguing), to show that someone has already reached the point of not wanting to continue.
N5 文法
まだ
Still
In English, まだ is regularly translated as 'still', or 'not yet', depending on if it is used in a positive non-past, or negative sentence. The reason that Japanese only requires one word for both of these nuances is due to the tense of the verb controlling the meaning, while まだ itself simply highlights the ongoing state.
These uses of まだ show the translation of 'still', but let's have a look at all of the possibilities below.

(Non-past) - The (A) state has not begun yet, but is expected to happen. 'Still' in English.

(ている) - The (A) state is continuing to happen. 'Still' in English.

(ていない) - The (A) state is continuing to not happen. 'Not yet' in English.

The negative form of this will be discussed more in まだ～ていません.

まだ is the opposite of もう, which will show that some state has ended.

まだ may also be used to ask questions. This is when the speaker thinks that something 'might' be continuing, but wants or needs to confirm.
Fun Fact

まだ is often used simply as an expression indicating that something is 'lacking', or 'not yet' where it needs to be. In these cases まだ is frequently repeated as まだまだ, for emphasis.
N5 文法
まだ～ていません
Still haven't done (something)
まだ～ていません is a regular expression that combines the adverb まだ, with the conjunction particle て. The て form will be followed by the verb いる in its negative いません (polite), or いない (casual) form. This expression has the meaning of 'to still not have done (A)'.
From these examples, it can be seen that this grammatical structure follows the regular rules of conjugation for the て form.
N5 文法

詳細

Let's compare the different ways to use もう and まだ, specifically focusing on why the verb form changes depending on the type of action.

Already?

When we say 'already', we are usually talking about one of two different things. Either a completed action, or a changed state. This is the same difference as we discussed in the previous Topic between ongoing actions versus ongoing resultant states.

For a verb which expresses a continuous action which has been completed, we simply use the past tense (た).

However, for instantaneous changes (things which have resultant states), ている is often used to show that the state of having been done is ongoing.

Another Aspect

Up until now we have mostly focused on もう, but what about まだ? When まだ is used to mean 'still', it shows that a situation is ongoing. For most verbs, this means まだ will be paired with ている (or ていない for negatives).

One major thing to watch out for is that stative verbs (verbs that inherently represent a state, like いる or ある) do not use ている. Because they already describe a state all on their own, they simply remain in their basic or polite form when paired with まだ.