Gítarinn hennar hljómar fallega í kvöld.

Because -inn is the suffixed definite article in Icelandic. So:

• gítar = guitar
• gítarinn = the guitar

In Icelandic, when you say something like her guitar, the noun is very often in the definite form, so gítarinn hennar is the normal pattern for her guitar.

That is the usual Icelandic pattern with possessives like hans, hennar, and þeirra. So Icelandic normally says:

• gítarinn hennar = her guitar

rather than putting hennar before the noun.

Also, hennar is the genitive form of hún (she), and here it means her. Unlike some other possessive words, hennar does not change form to match the gender or number of the thing possessed.

Hljómar is the 3rd person singular present tense of the verb hljóma.

So:

• hljóma = to sound
• hljómar = sounds

It is singular because the subject, gítarinn, is singular.

Because fallega is an adverb, while fallegur / falleg / fallegt are adjective forms.

Here, the sentence is describing how the guitar sounds, so Icelandic uses the adverb:

• fallegur = beautiful (adjective)
• fallega = beautifully / in a beautiful way (adverb)

With hljóma, Icelandic commonly uses the adverb: hljóma fallega.

It describes the sound, not the guitar’s appearance.

So Gítarinn hennar hljómar fallega means the guitar sounds beautiful.

If you wanted to say the guitar itself is beautiful to look at, you would say something like:

• Gítarinn hennar er fallegur. = Her guitar is beautiful.

That uses er (is) plus an adjective, not hljómar plus an adverb.

Í kvöld means tonight.

Literally, it is a prepositional time expression built with í + kvöld. Icelandic often uses expressions like this where English uses a single word such as tonight.

So in this sentence, í kvöld tells you when the guitar sounds beautiful.

Yes. The sentence as written has a very natural neutral order:

• Gítarinn hennar hljómar fallega í kvöld.

But Icelandic can move the time expression to the front for emphasis:

• Í kvöld hljómar gítarinn hennar fallega.

Notice that when something comes first, the finite verb hljómar still stays in second position. That is a very important pattern in Icelandic main clauses.

A rough English-style approximation is:

GEE-tah-rin HEN-nar HLYOH-mar FAHT-leh-ga ee KVOELT

A few notes:

• gí sounds like gee
• hlj in hljómar is tricky; it has no exact English equivalent, but you can think of it roughly as a breathy or voiceless ly
• fallega has the stress on the first syllable: FAL-
• kvöld has a rounded vowel that English does not really have, so an approximation is the best start

The main stress in Icelandic words is usually on the first syllable.