Le conducteur derrière nous n’aime pas attendre et appuie sur son klaxon.

In French, singular countable nouns usually need an article. So le conducteur means the driver.

You generally cannot say just conducteur by itself to mean driver in a normal sentence. French usually wants:

• le conducteur = the driver
• un conducteur = a driver

Derrière is a preposition here, and it is followed directly by a stressed pronoun like nous.

So you say:

• derrière nous = behind us
• devant moi = in front of me
• chez eux = at their place

You do not add de after derrière in this use.

After a preposition like derrière, French uses a stressed pronoun.

The stressed form for we/us is nous.

So:

• derrière nous = behind us
• avec nous = with us
• pour nous = for us

Nos is a possessive adjective meaning our, so it would need a noun after it, like nos amis.
On usually means one or informal we, but it is a subject pronoun, not the form used after derrière.

French negative sentences usually use ne ... pas around the verb:

• aime = likes
• n’aime pas = does not like

Before a vowel sound, ne becomes n’ for smoother pronunciation:

• ne aime pas → n’aime pas

This is called elision.

Standard French negation is normally built with two parts:

• ne before the verb
• pas after the verb

So:

• il aime = he likes
• il n’aime pas = he does not like

In everyday spoken French, people often drop ne, so you may hear:

• il aime pas

But in standard written French, ne ... pas is the normal form.

After aimer when it means to like doing something, the next verb stays in the infinitive.

So:

• aimer attendre = to like waiting
• aimer lire = to like reading
• aimer conduire = to like driving

This works much like English to like + -ing or to like + infinitive, but French uses the infinitive form.

Appuie is the il/elle/on form of the verb appuyer in the present tense.

The subject is Le conducteur, which is third person singular, so the verb must match that:

• j’appuie
• tu appuies
• il/elle/on appuie
• nous appuyons
• vous appuyez
• ils/elles appuient

So Le conducteur ... appuie is correct.

Because the same subject, Le conducteur, applies to both verbs:

• n’aime pas attendre
• et appuie sur son klaxon

French, like English, often does not repeat the subject when one subject does two actions:

• The driver doesn’t like waiting and presses his horn
• Le conducteur n’aime pas attendre et appuie sur son klaxon

You could repeat it, but it would sound heavier and less natural here.

The verb appuyer sur means to press on something.

So literally:

• appuie sur son klaxon = presses on his horn

In natural English, we might say presses his horn or more idiomatically honks his horn / leans on the horn, depending on context.

So sur is required by the French verb pattern appuyer sur quelque chose.

Son klaxon means his horn or the horn belonging to him/his vehicle.

French often uses a possessive adjective where English might also use the, especially when the owner is clear. But here son klaxon is very natural because it is specifically the driver’s horn.

Also, son agrees with the noun klaxon, which is masculine singular.

• son klaxon = his horn
• sa voiture = his/her car
• ses mains = his/her hands

Grammatically, son can mean his, her, or even its, depending on the owner.

It agrees with the thing owned, not with the owner’s gender.

Here:

• klaxon is masculine singular
• so French uses son

That does not tell you whether the driver is male or female by itself. In this sentence, le conducteur strongly suggests a male driver, so his horn is the natural translation.

Both can relate to driving, but they are not always interchangeable.

• conducteur = driver, the person operating the vehicle
• chauffeur = driver, often a professional driver, chauffeur, or in some contexts just driver

In a neutral sentence about a person driving a car, conducteur is very common and precise.

Yes. Klaxon is a normal French noun meaning car horn.

Originally, it came from a brand name, but in modern French it is just an everyday word.

So:

• un klaxon = a horn
• appuyer sur le klaxon = to press the horn
• faire retentir son klaxon = to sound one’s horn

Yes, most likely. The French present tense can describe an action happening now or a general situation.

In this sentence, it naturally sounds like a present scene:

• the driver behind us does not like waiting
• and he is pressing his horn

French often uses the present tense in exactly the same kind of way English does here.

Derrière is pronounced roughly like deh-RYEHR.

The final e is not a separate extra uh sound. The grave accent in -ière helps show the vowel quality.

A rough guide:

• derrière ≈ deh-RYEHR

Not exact English, of course, but that is a useful approximation.

Yes. Another natural possibility is to use klaxonner, which means to honk.

For example:

• Le conducteur derrière nous n’aime pas attendre et klaxonne.

That is a bit more direct than appuie sur son klaxon.
The version in your sentence is still completely natural and very understandable.