Kiedy usłyszeliśmy syrenę, pies schował się pod stołem i długo nie chciał wyjść.

Polish does not have articles like the and a/an.

So:

• pies can mean dog or the dog
• syrenę can mean a siren or the siren
• stół / stołem can mean a table / the table

Context tells you whether something is definite or indefinite. If Polish really wants to stress this/that specific one, it can use words like ten, but that is not required in a normal sentence like this.

Kiedy means when and introduces a time clause.

So Kiedy usłyszeliśmy syrenę means When we heard the siren.
That clause gives the time/background for the main action: the dog hid and did not want to come out.

This is an aspect question.

• usłyszeć = perfective, to hear at a specific moment, to catch the sound
• słyszeć = imperfective, to hear, to be hearing, to be able to hear

Here the sentence describes a single triggering moment: first we heard the siren, then the dog reacted. That is why usłyszeliśmy is natural.

Compare:

• Kiedy usłyszeliśmy syrenę... = when we heard the siren
• Słyszeliśmy syrenę... = we were hearing the siren / we could hear the siren

Usłyszeliśmy comes from the infinitive usłyszeć.

It is:

• past tense
• 1st person plural
• masculine-personal form

In Polish past tense, we-forms show gender:

• usłyszeliśmy = we heard, if the group includes at least one male
• usłyszałyśmy = we heard, if the speakers are all female

English does not show this distinction, but Polish does.

Because syrenę is the accusative singular form.

The noun syrena is feminine, and feminine nouns ending in -a often change to -ę in the accusative singular when they are direct objects.

Here syrenę is the direct object of usłyszeliśmy:

• syrena = nominative, dictionary form
• usłyszeliśmy syrenę = we heard the siren

Yes, syrena can mean both:

• siren as a warning sound
• mermaid

Context tells you which one is meant. Since the sentence says usłyszeliśmy (we heard), it clearly means siren here.

Schować się means to hide or more literally to hide oneself.

The particle się is often called reflexive, but in practice it is best to learn schować się as a whole expression.

Compare:

• schować coś = to hide / put away something
• schować się = to hide oneself, to hide

In English we usually just say the dog hid, not the dog hid itself, even though Polish uses się.

Because they agree with pies, which is a grammatically masculine noun.

In the singular, Polish past-tense verbs show gender:

• pies schował się = the dog hid
• suczka schowała się = the female dog hid

So even though English just says the dog, Polish grammar requires a masculine or feminine verb form depending on the noun used.

The preposition pod can take different cases:

• pod + accusative = movement to a place under something
  pod stół = under the table
• pod + instrumental = location under something
  pod stołem = under the table

In this sentence, pod stołem presents the dog's hiding place, so the phrase is understood as a location.

Also:

• stół = table
• stołem = instrumental singular of stół

You may also hear schować się pod stół when the speaker emphasizes the movement under the table, but schować się pod stołem is very natural when the focus is on where the dog ended up hiding.

Długo means for a long time.

Polish often expresses this idea with just the adverb, without a separate word corresponding to English for.

So:

• długo nie chciał wyjść = he did not want to come out for a long time

Again, this is about aspect.

• wyjść = perfective, one completed act of going/coming out
• wychodzić = imperfective, ongoing or repeated coming out / going out

Here the meaning is that the dog refused to do the single act of coming out, so wyjść is the natural choice.

Also, nie chciał wyjść means he didn’t want to come out.
If you said chciał nie wyjść, that would mean he wanted not to come out, which is a different structure and a different emphasis.

The basic meaning of wyjść is to go out / come out. English chooses go or come depending on point of view.

Here the dog is hiding under the table, and English naturally says come out in that situation. Polish uses wyjść either way.

So wyjść is not strictly only go out. Context decides the best English translation.

Because Kiedy usłyszeliśmy syrenę is a subordinate clause introduced by kiedy.

In Polish, subordinate clauses are normally separated from the main clause by a comma. So the comma here is standard punctuation.