شهادة الميلاد نسخة مصدقة وجاهزة.

A careful fully-vowelled MSA pronunciation is:

shahādatu l-mīlādi nuskhatun muṣaddaqatun wa-jāhizatun

Written with short vowels:

شهادةُ الميلادِ نسخةٌ مُصدَّقةٌ وجاهزةٌ

In everyday reading, learners often hear a lighter version with most case endings not pronounced:

shahādat al-mīlād nuskha muṣaddaqa wa-jāhiza

Because شهادة ends in ة (tāʾ marbūṭa).

• When a word with ة is said by itself, it usually sounds like -a / -ah:
  شهادة → shahāda
• But when it is followed by another word in a grammatical connection like this one, the t sound appears:
  شهادة الميلاد → shahādat al-mīlād

So this is very normal. English speakers often first learn ة as sounding like -a, then are surprised when it becomes -t in constructions like this.

Because Arabic usually omits is / are in present-tense nominal sentences.

So:

• شهادة الميلاد = the subject/topic
• نسخة مصدقة وجاهزة = the comment/predicate about it

Arabic simply puts them together and the meaning is is understood.

This is one of the most common differences from English. In past or future contexts, Arabic would usually use a verb such as كان.

This is an iḍāfa construction, often called a construct phrase.

It is made of:

• شهادة = certificate
• الميلاد = the birth / birth

Together, the phrase means literally something like certificate of birth, which English naturally expresses as birth certificate.

A key rule of iḍāfa:

• the first noun does not take ال
• the second noun can be definite or indefinite
• the whole phrase gets its definiteness from the second noun

So شهادة الميلاد is a definite phrase: the birth certificate.

Because in an iḍāfa construction, the first noun normally does not take الـ.

So Arabic says:

• شهادة الميلاد = the birth certificate

not:

• الشهادة الميلاد ✘

The definiteness comes from الميلاد, the second noun. Since that second noun is definite, the whole phrase is definite.

Because نسخة مصدقة وجاهزة is the predicate of the sentence, and predicate nouns are often indefinite in Arabic.

So the structure is:

• شهادة الميلاد = definite subject
• نسخة = indefinite predicate noun
• مصدقة وجاهزة = adjectives describing نسخة

Since نسخة is indefinite, its adjectives are also indefinite:

• نسخة = a copy
• مصدقة = certified
• جاهزة = ready

If you made them definite, you would be creating a different structure, more like the certified ready copy rather than the predicate of this sentence.

Because they agree with نسخة, which is feminine singular.

Arabic adjectives must agree with the noun they describe in:

• gender
• number
• definiteness

Here:

• نسخة is feminine singular and indefinite
• so the adjectives are also feminine singular and indefinite:
  • مصدقة
  • جاهزة

That is why you do not see the masculine forms مصدق or جاهز here.

It is functioning as an adjective here, and more specifically it is a passive participle.

It comes from the verb صدّق in the sense of to certify / authenticate.

So:

• مُصَدَّق = certified, authenticated (masculine)
• مُصَدَّقة = certified, authenticated (feminine)

Because it describes نسخة feminine singular, it appears as مصدقة.

So you can think of it as meaning certified.

It simply means and.

So:

• مصدقة = certified
• وجاهزة = and ready

Both adjectives describe نسخة.

So the phrase means:

• a certified and ready copy

Grammatically, Arabic often links multiple adjectives with و just like English uses and.

In fully vocalized formal MSA, the sentence is:

شهادةُ الميلادِ نسخةٌ مُصدَّقةٌ وجاهزةٌ

The endings are:

• شهادةُ = nominative, because it is the subject of the nominal sentence
• الميلادِ = genitive, because it is the second term of the iḍāfa
• نسخةٌ = nominative, because it is the predicate
• مُصدَّقةٌ and جاهزةٌ = nominative, because they follow نسخة

But in normal Arabic writing, these short-vowel endings are usually not written. Learners still need to understand them, but native readers usually read unvowelled text without any problem.