Hún talar kurteislega við þjóninn.

It follows a very common Icelandic pattern:

Hún = subject
talar = finite verb
kurteislega = adverb
við þjóninn = prepositional phrase

So the sentence is basically:

Subject + Verb + Adverb + Prepositional phrase

In a neutral main clause, this is very natural Icelandic word order.

Because tala is the infinitive, meaning to speak / to talk.

Here you need the present-tense form that matches hún (she), so Icelandic uses talar:

• ég tala = I speak
• þú talar = you speak
• hún talar = she speaks

So talar is the correct finite form for hún.

Usually it can mean either, depending on context.

So Hún talar kurteislega við þjóninn can mean:

• She speaks politely to the waiter
• She is speaking politely to the waiter

If Icelandic wants to make the ongoing action extra explicit, it can use vera að + infinitive:

Hún er að tala kurteislega við þjóninn = She is speaking politely to the waiter

Because it is an adverb, and it describes how she speaks.

• kurteislega = politely / courteously

A very common Icelandic adverb ending is -lega, which often works a bit like English -ly.

So here:

• talar = speaks
• kurteislega = politely

The adverb modifies the verb, not the noun.

This is a very common learner question.

With the verb tala, Icelandic normally uses við for the person you are speaking to:

• tala við einhvern = talk/speak to someone

So in this sentence:

• við þjóninn = to the waiter

Even though við can sometimes look like with in English, in this expression the best translation is usually to or with, depending on natural English style.

Because þjóninn is the accusative singular definite form, and við takes the accusative.

The dictionary form is:

• þjónn = waiter

Its definite forms include:

• þjónninn = the waiter in the nominative
• þjóninn = the waiter in the accusative

Since the sentence has við þjóninn, the noun must be in the accusative, so þjóninn is correct.

This is also a good example of Icelandic case affecting the form of the noun.

It is attached to the noun.

Icelandic usually uses a suffixed definite article rather than a separate word like English the.

So:

• þjónn = waiter
• þjóninn = the waiter

The -inn part is the definite article here.

This is one of the big differences from English, and learners notice it very quickly.

Yes, but the given sentence is the most neutral order.

Icelandic main clauses follow the verb-second principle, which means the finite verb normally stays in second position. If you move another element to the front for emphasis, the verb still stays second.

For example, a more marked version could be:

Við þjóninn talar hún kurteislega.

That still means roughly the same thing, but now við þjóninn is being highlighted.

For a beginner, Hún talar kurteislega við þjóninn is the safest and most natural pattern to copy.

A few useful pronunciation points:

• ú in Hún sounds roughly like oo in moon
• ð in við sounds roughly like th in this
• þ in þjóninn sounds roughly like th in thin
• ei in kurteislega sounds roughly like ay in day

Also, Icelandic stress usually falls on the first syllable of the word, so:

• HÚN
• TA-lar
• KUR-teis-lega
• VIÐ
• ÞJÓ-ninn

That first-syllable stress is very important for sounding natural.