В тихом лесу шумят деревья.

Because в тихом лесу means in the quiet forest, so лес is in the prepositional case after в when talking about location.

• в + prepositional = in / at a place
• лес → в лесу
• тихий → тихом to agree with лесу

So:

• в тихом лесу = in the quiet forest

By contrast:

• в тихий лес would use the accusative case and would mean into the quiet forest, showing motion toward a place.
• в тихом лесе sounds unnatural in standard modern Russian here. For лес, the usual prepositional form after в is в лесу.

This is a common pattern with some masculine nouns in Russian. The noun лес has the prepositional singular form лесу in this meaning.

So the forms are:

• лес = forest
• в лесу = in the forest

This is something learners often just need to memorize. A few common words behave similarly:

• сад → в саду
• порт → в порту
• угол → в углу

So в лесу is a very normal fixed form in Russian.

Тихом is the form of the adjective тихий that matches the noun лесу.

Russian adjectives must agree with the nouns they describe in:

• gender
• number
• case

Here, лесу is:

• masculine
• singular
• prepositional

So тихий changes to тихом.

This gives:

• тихий лес = a quiet forest
• в тихом лесу = in a quiet forest / in the quiet forest

Because the subject is деревья, which is plural.

• дерево = tree
• деревья = trees

Russian verbs in the present tense agree with the subject in number and person.

So:

• дерево шумит = the tree is making noise / rustling
• деревья шумят = the trees are making noise / rustling

That is why the verb is шумят, not шумит.

Деревья is the nominative plural of дерево.

It is the subject of the sentence, so it appears in the nominative case.

Forms:

• дерево = tree
• деревья = trees

Since деревья is doing the action, it stays in the nominative plural.

Here шумят means something like:

• make noise
• rustle
• murmur
• sway noisily in the wind

With деревья, the meaning is usually not that the trees are making an artificial or harsh noise. It often suggests the natural sound of leaves and branches in the wind.

So in this sentence, шумят is very natural and poetic.

Because Russian present-tense verbs already contain the idea of am / is / are when needed.

• шумят already means they make noise / they are making noise

Russian does not need a separate present-tense form of to be in a sentence like this.

So:

• деревья шумят literally works as trees rustle / the trees are rustling

Russian word order is flexible. Starting with в тихом лесу puts the setting first:

• In the quiet forest, the trees are rustling.

This order sounds natural because it first establishes the place, then tells what is happening there.

You could also say:

• Деревья шумят в тихом лесу.

That is also grammatical, but it places a little more attention on деревья first. The original version feels a bit more descriptive and scene-setting.

It looks irregular because the plural of дерево is not made by simply adding a regular ending.

• дерево → деревья

This is a normal Russian plural pattern for some neuter nouns ending in -о.

A rough pronunciation guide:

• де-ре-вья

The вья part can be tricky for English speakers because of the soft consonant plus я. It helps to think of it as a blended sound rather than pronouncing every letter separately.

Russian does not have articles like a or the, so the sentence itself does not explicitly mark definiteness.

Depending on context, в тихом лесу шумят деревья could mean:

• In a quiet forest, trees are rustling
• In the quiet forest, the trees are rustling

English has to choose a/the, but Russian does not. The context tells you which interpretation is more natural.