Нужно подшить брюки.

Нужно means it is necessary, one needs to, or it’s needed.

In Нужно подшить брюки, the idea is:

It is necessary to hem the trousers
or more naturally in English, The trousers need to be hemmed.

This is a very common Russian impersonal construction:

• Нужно + infinitive
• Надо + infinitive works similarly

For example:

• Нужно идти. = We/I/one need(s) to go.
• Нужно позвонить. = It’s necessary to call.

Because this is an impersonal sentence.

Russian often leaves out the person responsible when the main idea is simply that something needs to be done. English often does something similar with phrases like:

• It’s necessary to...
• You need to...
• This needs to be...

So Нужно подшить брюки does not say exactly who must do it. Depending on context, it could mean:

• I need to hem the trousers
• We need to hem the trousers
• The trousers need hemming
• Someone needs to hem the trousers

Russian is comfortable leaving that unspecified.

Because after нужно, Russian normally uses an infinitive to describe the required action.

So the structure is:

нужно + infinitive + object

Here:

• нужно = necessary / need to
• подшить = to hem
• брюки = trousers

This is why you do not say a finite verb like подшивает here.

Compare:

• Нужно подождать. = It is necessary to wait.
• Нужно купить хлеб. = We need to buy bread.

Подшить is the perfective form, while подшивать is imperfective.

In this sentence, подшить is used because the focus is on a single completed result: the trousers should end up hemmed.

So:

• Нужно подшить брюки = The trousers need to be hemmed / We need to hem the trousers
  Focus: get the job done.

If you used подшивать, it would sound more like talking about the process, habit, or general activity:

• Я умею подшивать брюки. = I know how to hem trousers.
• Она подшивает одежду. = She hems clothes.

After нужно, both aspects are possible in some contexts, but perfective is very common when you mean do this once and complete it.

Not exactly.

The base verb is шить = to sew.

But подшить has a more specific meaning: to hem, especially by folding and sewing the edge of fabric, often to shorten clothing a little.

So with брюки, подшить usually means:

• to hem the trousers
• to take up the trousers

This is more specific than just sew.

In this word, под- helps create the meaning to hem / sew up the edge / take up slightly.

Prefixes in Russian often change the basic meaning of a verb in ways that are not always fully predictable from the literal meaning of the prefix alone. So while под- often has meanings like under, up to, or slightly, in подшить you should learn the whole verb as a vocabulary item:

• шить = to sew
• подшить = to hem / take up
• подшивать = to be hemming / to hem regularly

So it is best not to interpret it too mechanically as simply sew under.

Because брюки is one of those Russian nouns that is normally used only in the plural, like English trousers, pants, or scissors.

So:

• брюки = trousers / pants

Russian treats this as a plural noun even when referring to one garment.

Other similar Russian nouns include:

• ножницы = scissors
• очки = glasses
• часы = clock/watch

So брюки is grammatically plural, even though in meaning it refers to one item of clothing.

It is in the accusative plural, because it is the direct object of подшить.

We are hemming what?
брюки

For inanimate plural nouns like брюки, the accusative plural is usually the same as the nominative plural. So the form stays:

• nominative: брюки
• accusative: брюки

That is why you do not see any ending change here.

Yes, absolutely.

Надо подшить брюки and Нужно подшить брюки are both natural.

Broadly speaking:

• надо is often a bit more conversational and common in everyday speech
• нужно can sound slightly more neutral or formal

In many situations, they are interchangeable.

You can also add a person if needed:

• Мне нужно подшить брюки. = I need to hem the trousers / My trousers need hemming.
• Тебе надо подшить брюки. = You need to hem the trousers.

No, Russian word order is fairly flexible.

Нужно подшить брюки is a very neutral order.

You could also say:

• Брюки нужно подшить.
• Подшить нужно брюки.

But the emphasis changes a little:

• Нужно подшить брюки = neutral statement
• Брюки нужно подшить = emphasizes the trousers
• Подшить нужно брюки = emphasizes the action hemming, often in contrast to some other action

So the original sentence is probably the most natural default version.

The stress is:

• ну́жно
• подши́ть
• брю́ки

So the full sentence is pronounced roughly as:

Ну́жно подши́ть брю́ки.

A few pronunciation notes:

• In брюки, the ю gives a yu sound.
• In подшить, the ш is a hard sh sound.
• The final -ть in подшить is the normal infinitive ending.

Yes. In clothing contexts, that is often exactly how it would be translated naturally.

Depending on context, Нужно подшить брюки can mean:

• The trousers need to be hemmed
• The trousers need to be taken up
• We need to shorten the trousers by hemming them

So while the core idea is hem, in practical English the best translation may be take up the trousers, especially if the issue is length.