Для поездки ей понадобилась справка с работы и копия паспорта.

Because the preposition для always takes the genitive case.

• поездка = trip
• для поездки = for the trip

So поездки is the genitive singular form of поездка.

Ей is the dative form of она.

With the verb понадобиться, Russian marks the person who needs something in the dative:

• ей понадобилась... = she needed...
• literally: to her, ... was needed

So она would not work here, because она is nominative, but this verb wants кому? — the dative.

Понадобилась is the past tense, feminine singular form of понадобиться.

This verb means something like:

• to be needed
• to turn out to be necessary
• to be required

A very literal breakdown is:

• ей понадобилась справка = a certificate became necessary to her

But in natural English, that is simply:

• she needed a certificate

Compared with нужна была, понадобилась often sounds a bit more like a requirement came up or turned out to be necessary.

The grammatical subject is not ей.

The things that were needed are the subject:

• справка
• копия паспорта

That is why the verb agrees with those nouns, not with ей.

So although English says she needed..., Russian structures it more like:

• to her was needed a certificate and a copy of a passport

This is a very common learner question.

You might expect the plural понадобились, because there are two nouns joined by и. And yes, понадобились is also possible.

But when the verb comes before a compound subject in Russian, singular agreement with the nearest noun is quite common.

Here the nearest noun is:

• справка — feminine singular

So the sentence uses:

• понадобилась справка с работы и копия паспорта

If you put the subject first, plural usually feels more expected:

• Справка с работы и копия паспорта ей понадобились.

So:

• понадобилась = natural with this word order
• понадобились = also possible, especially if you want to treat both items equally

Справка с работы is an official note or certificate from your employer.

Depending on context, it may confirm things like:

• that you are employed there
• your job title
• your salary
• your dates of employment
• that you have approved leave

In travel, visa, or bureaucratic contexts, справка с работы is a very common phrase.

Because Russian normally says с работы for from work / from one’s workplace.

This is the standard idiomatic expression:

• я пришёл с работы = I came from work
• справка с работы = a certificate from work

Из работы is not used in this meaning.

Because копия is followed by the genitive:

• копия чего? — паспорта

This is a very common pattern in Russian:

• копия паспорта = copy of a passport
• страница книги = page of a book
• часть фильма = part of a film

So паспорта is genitive singular after копия.

Russian often leaves out possessive words when the owner is obvious from context.

Here ей already tells us that the required documents are connected with her, so:

• копия паспорта naturally means a copy of her passport

If you needed extra emphasis or wanted to avoid ambiguity, you could say:

• копия её паспорта

But in this sentence, that would usually be unnecessary.

It puts the purpose or context first:

• Для поездки = for the trip

Russian word order is flexible, so starting with this phrase is very natural. It tells the listener right away what situation the sentence is about.

Other word orders are also possible:

• Ей для поездки понадобилась справка с работы и копия паспорта.
• Справка с работы и копия паспорта ей понадобились для поездки.

The core meaning stays the same, but the emphasis changes.

Russian has no articles like a and the.

So Russian does not directly mark that distinction. Instead, you understand it from context.

In this sentence, English normally uses:

• a certificate from work and a copy of her passport

because the sentence is presenting them as required documents, not referring back to specific ones already mentioned.