Við kveikjum á hljóðkerfinu, en hljóðstyrkurinn er of hár.

Kveikjum is the present tense, 1st person plural form of the verb kveikja.
So við kveikjum = we turn on / we switch on / we light (up) (depending on context).
Conjugation (present):

• ég kveiki
• þú kveikir
• hann/hún/það kveikir
• við kveikjum
• þið kveikið
• þeir/þær/þau kveikja

In Icelandic, kveikja á is a common verb + particle pattern meaning to switch/turn something on.
So:

• kveikja á X = turn on X
  And the opposite is:
• slökkva á X = turn off X

The á is not optional here in normal usage; kveikja alone often means ignite/light (like lighting a candle), while kveikja á is the everyday “switch on” expression.

Because kveikja á governs the dative case for the thing being switched on.
So hljóðkerfi (a neuter noun) appears in dative singular definite:

• nominative: hljóðkerfi
• accusative: hljóðkerfi
• dative: hljóðkerfi
• dative + definite: hljóðkerfinu

That’s why you get á hljóðkerfinu.

-inu is the definite article suffix in the dative singular for many neuter nouns.
Here it marks the sound system (specific/known), and the dative required by á (in this usage).

Roughly:

• hljóðkerfi = (a) sound system
• hljóðkerfið = the sound system (nominative/accusative)
• hljóðkerfinu = to/on/with the sound system (dative, depending on the verb/preposition)

Icelandic usually expresses the with a suffix attached to the noun (a “postposed definite article”).
So:

• hljóðstyrkur = (a) volume
• hljóðstyrkurinn = the volume

You can also use a separate demonstrative-like word (þessi/sá) when needed, but the default “the” is typically the suffix.

Because they’re different nouns with different gender and case here:

• hljóðkerfi is neuter, and it’s in the dative → hljóðkerfinu
• hljóðstyrkur is masculine, and it’s in the nominative (as the subject of er) → hljóðstyrkurinn

The definite endings vary by gender + case.

Because the clause hljóðstyrkurinn er of hár follows the common pattern:

• [subject in nominative] + er + [adjective]

Here, er is the present tense of vera (to be), and the noun in nominative (hljóðstyrkurinn) is the subject.

The adjective must agree with the noun hljóðstyrkurinn in gender, number, and case.
hljóðstyrkur is masculine singular nominative, so the adjective is:

• masculine nominative singular: hár

Hátt would be used when describing something neuter (or used as an adverb-like form in some contexts), but here the grammar is clearly adjective agreement with a masculine noun.

Of means too (excessively). It normally comes right before the adjective/adverb it modifies:

• of hár = too high
  So hljóðstyrkurinn er of hár = the volume is too high.

En means but and commonly introduces a contrast:

• We turn it on, but the volume is too high.

The comma before en is standard here because it separates two independent clauses:

• Við kveikjum á hljóðkerfinu, (clause 1)
• en hljóðstyrkurinn er of hár. (clause 2)

Grammatically it’s present tense. Depending on context, Icelandic present tense can cover:

• habitual: We (usually) turn on the sound system...
• right now: We’re turning on the sound system...
• near future / intention (context-driven): We’re going to turn on the sound system...

If you need to be explicit about intention, you might use other constructions, but the plain present is often enough in conversation.

A rough guide (dialects vary):

• hljóð: the hlj- is like an l with breathy h before it; jó is like yo; ð is a soft “th” sound (often very light in speech).
• hljóðkerfinu: stress on the first syllable: HLJÓÐ-ker-fi-nu.
• hljóðstyrkurinn: stress on the first syllable: HLJÓÐ-styrk-ur-inn.

Key pronunciation notes:

• Icelandic stress is almost always on the first syllable.
• y in styrk- is a front rounded vowel (not English i); many learners approximate it at first.