Для теста нужны мука, молоко и дрожжи.

Because the preposition для always takes the genitive.

So:

• для = for
• тесто = dough
• для теста = for the dough

The dictionary form is тесто, and its genitive singular form is теста.

A learner might notice that теста could also come from тест (test), but in this sentence the meaning is clearly dough, not test.

Нужны agrees with the things that are needed: мука, молоко и дрожжи.

Since that is a plural list, Russian uses the plural form:

• нужен = needed (masculine singular)
• нужна = needed (feminine singular)
• нужно = needed (neuter singular)
• нужны = needed (plural)

Even though the nouns have different genders:

• мука — feminine
• молоко — neuter
• дрожжи — plural-only

the whole group is treated as plural, so нужны is the correct form.

Because they are the grammatical subject of the sentence.

Russian structures this idea as:

For the dough, flour, milk, and yeast are needed.

So the things being needed are:

• мука
• молоко
• дрожжи

That is why they stay in the nominative.

This is different from English, where learners may mentally start from something like We need flour, milk, and yeast. In that English structure, those words are objects. But in Russian, this sentence is built differently.

Not exactly. It is the short form of the adjective нужный (needed, necessary), used as a predicate.

So this sentence does not literally use a normal verb meaning need. Instead, it uses a structure closer to:

Flour, milk, and yeast are necessary / are needed for the dough.

In the present tense, Russian usually leaves out есть (is/are), so:

• Для теста нужны мука, молоко и дрожжи.

literally feels like:

• For the dough needed are flour, milk, and yeast.

Russian word order is flexible, and the beginning of the sentence often shows the topic or background.

Starting with Для теста means something like:

As for the dough... or For the dough...

Then the sentence tells you what is needed for it.

You could also say:

• Мука, молоко и дрожжи нужны для теста.

This means the same thing, but the emphasis is a little different. The original version sounds natural when you are listing ingredients or explaining a recipe.

Дрожжи is normally a plural-only noun in Russian.

That means Russian treats yeast like a plural item, similar to how English treats words like scissors or pants.

So you usually say:

• дрожжи
• not a normal singular form in everyday use for the baking ingredient

This is one reason нужны sounds natural here, though the list as a whole would already require plural agreement anyway.

Yes. That is a very natural English translation.

But grammatically, the Russian sentence is not built the same way. Russian is saying more literally:

For the dough, flour, milk, and yeast are needed.

So the meaning matches We need flour, milk, and yeast for the dough, even though the grammar is different.

Russian has no articles like a, an, or the.

So:

• мука can mean flour, the flour, or sometimes some flour
• молоко can mean milk, the milk, or some milk
• дрожжи can mean yeast, the yeast, or some yeast

Context tells you how specific the meaning is. In a recipe context, English usually just says flour, milk, and yeast, which matches the Russian well.

Because in a simple list, Russian normally does not put a comma before и when it means and.

So:

• мука, молоко и дрожжи

is exactly what you would expect for flour, milk, and yeast.

This is standard Russian punctuation.