Hvolpurinn sefur.

It is the definite article attached to the noun, so it marks hvolpurinn as the puppy rather than just a puppy / puppy.

A very common Icelandic pattern is:

• hvolpur = puppy
• hvolpurinn = the puppy

Unlike English, Icelandic usually puts the at the end of the noun instead of using a separate word.

The dictionary form is hvolpur.

That is the basic singular form you would look up in a dictionary.
Hvolpurinn is that noun with the definite article added.

Also, hvolpur is a masculine noun, which matters because Icelandic noun endings change according to gender, number, and case.

It is in the nominative singular.

Why? Because it is the subject of the sentence, and subjects are usually in the nominative case in Icelandic.

So in this sentence:

• hvolpurinn = subject
• sefur = verb

This is one of the first important things to notice in Icelandic: nouns change form depending on their grammatical role.

Because sofa is the infinitive, meaning the basic dictionary form to sleep.
In the sentence, the verb has to be conjugated.

Sefur is the present tense, 3rd person singular form.

A few present-tense forms of sofa are:

• ég sef = I sleep / I am sleeping
• þú sefur = you sleep / you are sleeping
• hann/hún/það sefur = he/she/it sleeps / is sleeping

So hvolpurinn sefur uses the 3rd person singular because the puppy is a singular subject.

This is a normal kind of Icelandic verb change. Some verbs change their stem vowel when they are conjugated.

So with sofa:

• infinitive: sofa
• 1st person singular present: sef
• 3rd person singular present: sefur

This kind of vowel change is something you simply learn as part of the verb’s pattern. It is very common in Icelandic and not something unusual about this sentence.

It can mean either one, depending on context.

So Hvolpurinn sefur could mean:

• The puppy sleeps in a general sense
• The puppy is sleeping right now

Icelandic often uses the simple present where English might choose either sleeps or is sleeping.

If you want to strongly emphasize an ongoing action, Icelandic can also use:

• Hvolpurinn er að sofa = The puppy is sleeping

But Hvolpurinn sefur is perfectly normal.

Because hvolpurinn already is the subject.

English sometimes repeats subjects in different ways, but Icelandic does not need an extra pronoun here. The noun itself does the job:

• Hvolpurinn = subject
• sefur = verb

So the sentence is complete as it is.

Yes, but Hvolpurinn sefur is the most neutral, straightforward order for a statement.

Icelandic word order is fairly flexible, but the verb often stays in an important early position. For example:

• Hvolpurinn sefur. = The puppy sleeps / is sleeping.
• Sefur hvolpurinn? = Is the puppy sleeping?
• Núna sefur hvolpurinn. = Now the puppy is sleeping.

So the order can change, but the version you have is the basic declarative pattern.

A rough English-friendly guide would be:

• hvolpurinn ≈ KVOL-pur-rin
• sefur ≈ SEH-vur

A few helpful notes:

• Stress is usually on the first syllable in Icelandic words.
• hv in modern Icelandic is often pronounced close to kv.
• The r is not like a typical English r; it is usually tapped or trilled.
• The vowel written u in Icelandic is not exactly like English u.

So an approximate rhythm would be:

KVOL-pur-rin SEH-vur

Yes, but it would not mean exactly the same thing.

• Hvolpurinn sefur = the puppy sleeps
• Hvolpur sefur = a puppy / puppy sleeps, depending on context

So the presence of -inn makes the noun definite. That is one of the main things this sentence teaches: Icelandic often marks definiteness by adding an ending to the noun itself.