Таможенная декларация уже готова.

Because готова is the short form of the adjective готовый (ready).

In Russian, short-form adjectives are often used:

• as part of the predicate, after an implied to be
• to describe a temporary state or condition

So:

• Таможенная декларация уже готова. = The customs declaration is already ready.

Compare:

• готовая декларация = a ready/finished declaration
  
  • here готовая is the full form, used before a noun
• декларация готова = the declaration is ready
  
  • here готова is the short form, used as the predicate

Since декларация is feminine singular, the short form is готова.

The ending -а shows that the short-form adjective agrees with a feminine singular noun.

The noun декларация is feminine, so the adjective must match it:

• masculine: готов
• feminine: готова
• neuter: готово
• plural: готовы

Examples:

• Документ готов. = The document is ready.
• Декларация готова. = The declaration is ready.
• Письмо готово. = The letter is ready.
• Документы готовы. = The documents are ready.

In the present tense, Russian usually does not use a verb meaning is/are/am.

So English:

• The customs declaration is already ready

becomes Russian:

• Таможенная декларация уже готова.

Russian simply puts the subject and the predicate together, without a present-tense to be.

In other tenses, Russian does use forms of быть:

• Таможенная декларация была готова. = The customs declaration was ready.
• Таможенная декларация будет готова. = The customs declaration will be ready.

Уже means already.

In this sentence, it comes before готова:

• Таможенная декларация уже готова.

That is a very natural placement. It highlights the idea that the declaration is ready now, perhaps earlier than expected or after some waiting.

Russian word order is flexible, so you may also see:

• Уже таможенная декларация готова.
• Таможенная декларация готова уже.

But the most neutral and common version here is:

• Таможенная декларация уже готова.

It is in the nominative case.

This is because Таможенная декларация is the subject of the sentence:

• The customs declaration is already ready.

You can recognize the nominative feminine singular endings here:

• таможенная
• декларация

Both words agree in:

• gender: feminine
• number: singular
• case: nominative

Таможенная comes from таможенный, which means customs-related or pertaining to customs.

So:

• таможенная декларация = customs declaration

The adjective agrees with декларация, which is feminine singular, so:

• masculine: таможенный
• feminine: таможенная
• neuter: таможенное
• plural: таможенные

You may also meet related phrases like:

• таможенный контроль = customs control
• таможенная служба = customs service
• таможенные правила = customs regulations

Декларация is pronounced approximately:

de-kla-RA-tsi-ya

The stress is on ра:

• декларАция

A rough English approximation would be:

• dyek-la-RA-tsi-ya

A few pronunciation notes:

• unstressed е often sounds closer to i/ye
• ц sounds like ts
• я at the end sounds like ya

A natural pronunciation is approximately:

ta-MO-zhin-na-ya de-kla-RA-tsi-ya u-ZHE ga-TO-va

Stress:

• тамОженная
• декларАция
• ужЕ
• готОва

A few useful notes:

• ж sounds like the s in measure
• unstressed vowels are often reduced, so spoken Russian may sound less clear-cut than the spelling suggests
• г in готова is a hard g, as in go

Yes. Russian word order is more flexible than English word order.

The neutral order here is:

• Таможенная декларация уже готова.

But other orders are possible for emphasis:

• Уже готова таможенная декларация.
  This can sound like The customs declaration is already ready with more focus on the result.

• Таможенная декларация готова уже.
  This is possible, but often feels more marked or conversational.

• Готова уже таможенная декларация.
  This is also possible in context, especially if you are contrasting it with something else.

For learners, the safest default is:

• Таможенная декларация уже готова.

It can be used for both.

For things:

• Декларация готова. = The declaration is ready.
• Еда готова. = The food is ready.

For people:

• Я готов. = I am ready.
• Я готова. = I am ready.
  (said by a woman)
• Мы готовы. = We are ready.

So готов and its forms describe readiness in general, whether the subject is a person, object, document, meal, and so on.

Yes, but it is not exactly the same.

• готова means ready
• сделана means done/made/completed

So:

• Таможенная декларация уже готова.
  = The customs declaration is already ready.

• Таможенная декларация уже сделана.
  = The customs declaration has already been done/completed.

In many contexts they may be close in meaning, but готова focuses on the state of being ready, while сделана focuses more on the fact that the work has been completed.

Because таможенная is an adjective modifying декларация, and Russian adjectives must agree with the noun they describe.

Since декларация is:

• feminine
• singular
• nominative

the adjective must also be:

• feminine
• singular
• nominative

So:

• таможенная декларация

If the noun changed, the adjective would change too:

• таможенный документ = customs document
• таможенное оформление = customs clearance/formalities
• таможенные документы = customs documents

This agreement is one of the most important features of Russian grammar.