Dýraathvarfið er opið í dag.

It is a compound word:

• dýra = of animals
• athvarf = shelter or refuge
• -ið = the (the suffixed definite article)

So dýraathvarfið literally means the shelter of animals, which is the natural Icelandic way to say the animal shelter.

Compounds like this are very common in Icelandic.

Because dýra is the genitive plural form of dýr.

In Icelandic compounds, the first noun is often put into a genitive form to show a relationship like of animals. So:

• dýr = animal / animals
• dýra- = animal-, animals', of animals

That is why dýraathvarf is built the way it is.

That -ið is the definite article attached to the end of the noun.

Unlike English, Icelandic usually says the by adding it to the word itself. So:

• athvarf = a shelter / shelter
• athvarfið = the shelter

Because athvarf is a neuter noun, the definite ending here is -ið.

Because the adjective has to agree with dýraathvarfið, which is neuter singular.

The basic dictionary form is usually opinn for the masculine singular, but the forms change:

• opinn = masculine
• opin = feminine
• opið = neuter

Since dýraathvarfið is neuter, Icelandic uses opið.

Also, after er in a sentence like this, Icelandic normally uses the predicative adjective form, so dýraathvarfið er opið is exactly what you would expect.

Er means is. It is the present tense of vera, the verb to be.

So the structure is:

• Dýraathvarfið = the animal shelter
• er = is
• opið = open
• í dag = today

This is a very straightforward Icelandic sentence pattern: subject + er + adjective + time expression.

Í dag means today.

Literally, it is in day, but you should learn it as a fixed expression meaning today.

• í = in
• dag = day, here in the required case form

This is one of the most common Icelandic time expressions:

• í dag = today
• í gær = yesterday

So even though English uses a single word, Icelandic uses this prepositional phrase.

Yes. The sentence Dýraathvarfið er opið í dag is perfectly normal, but you can also say:

Í dag er dýraathvarfið opið.

That version puts extra focus on today.

In Icelandic, when something other than the subject comes first, the finite verb still usually stays in the second position, so er comes right after Í dag.

A rough English-friendly approximation is:

DEE-ra-ath-var-vith er OH-pith ee dahg

A few helpful points:

• Stress in Icelandic usually falls on the first syllable of each word.
• ý is roughly like the vowel in see, though not exactly the same.
• ð is like the th in this.
• í is a long ee sound.

This is only an approximation, but it is a useful starting point.

Not necessarily. By itself, Dýraathvarfið er opið í dag simply states that the animal shelter is open today.

It does not automatically mean:

• that it is unusual,
• that it is only open today,
• or that it is normally closed.

Any extra implication would depend on context. The sentence itself is just a neutral statement about today.