Sumarbústaðurinn er tilbúinn.

In Icelandic, the definite article the is usually attached to the end of the noun instead of written as a separate word.

So:

• sumarbústaður = summer house / summer cottage
• sumarbústaðurinn = the summer house / the summer cottage

The ending -inn here is the masculine singular nominative definite ending.

The dictionary form is sumarbústaður.

It is made up of:

• sumar = summer
• bústaður = residence, dwelling, place to stay

So sumarbústaður literally means something like summer residence, which is why it is translated as summer house or summer cottage.

Icelandic uses compounds very freely, much more than English often does.

So where English says summer house, Icelandic commonly makes a single compound noun:

• sumar
  • bústaður → sumarbústaður

This is completely normal in Icelandic. English learners often want to split such words up, but in Icelandic one-word compounds are very common.

Er is the present tense singular form of the verb vera, which means to be.

So:

• ég er = I am
• þú ert = you are
• hann/hún/það er = he/she/it is

In this sentence, er means is.

Because Icelandic adjectives must agree with the noun they describe in gender, number, and case.

Here, sumarbústaðurinn is:

• masculine
• singular
• nominative

So the adjective also takes the masculine singular nominative form:

• masculine: tilbúinn
• feminine: tilbúin
• neuter: tilbúið

That is why the sentence uses tilbúinn.

Usually, yes. In this sentence, tilbúinn means ready.

Depending on context, it can also suggest:

• prepared
• finished
• set
• all set

But ready is the most natural basic meaning here.

Because this sentence uses a very common pattern:

• subject + vera + adjective

So:

• Sumarbústaðurinn = subject
• er = is
• tilbúinn = adjective describing the subject

This is like English The summer house is ready. The adjective comes after is because it is part of the predicate, not directly placed before the noun.

It is in the nominative case because it is the subject of the sentence.

In simple statements with to be, the thing doing or being something is usually in the nominative:

• Sumarbústaðurinn = nominative subject
• er tilbúinn = is ready

This is also why the adjective is in the nominative form.

Yes, bústaður is a masculine noun.

One clue is its dictionary ending -ur, which is very common for masculine nouns in Icelandic, although not every noun ending in -ur is masculine and not every masculine noun ends in -ur. Still, it is a useful clue.

Because the noun is masculine, the definite form and the adjective both show masculine agreement:

• sumarbústaðurinn
• tilbúinn

A rough English-friendly guide would be something like:

• SUH-mar-boo-sta-thur-rinn

A few important notes:

• Stress is usually on the first syllable in Icelandic: SUmarbústaðurinn
• ú sounds like oo
• ð is like the th in this, not the th in thin
• The ll-type sound is not present here, so this word is easier than many Icelandic ones
• The ending -urinn / -inn should be pronounced clearly, not swallowed

This is only an approximation, but it helps get close.

Because it is the first word of the sentence.

In Icelandic, nouns are not capitalized just because they are nouns. That is different from German. So the dictionary form is normally written:

• sumarbústaður
• tilbúinn

But at the beginning of a sentence, Sumarbústaðurinn gets a capital S.

Yes, if the context already makes it clear which cottage or house you mean.

• Sumarbústaðurinn er tilbúinn = The summer house is ready
• Bústaðurinn er tilbúinn = The house/residence/cottage is ready

The full compound is more specific. The shorter version is possible if the meaning is already understood from context.