Learn Hardcore Icelandic: Ég klára heimavinnuna áður en ég fer að sofa. - I finish the homework before I go to sleep.

The base noun is heimavinna = homework (feminine).
Definite form (nominative): heimavinnan = the homework.
In this sentence, heimavinna is the direct object of klára (to finish), so it takes the accusative.
Feminine nouns often add -na in the definite accusative singular: heimavinnuna.

So Ég klára heimavinnuna literally is I finish the homework (which in English we’d usually say as my homework).

Why is it áður en and not just áður?

áður by itself is an adverb meaning before, earlier:
- Ég borða áður. – I eat earlier / beforehand.
áður en is a conjunction meaning before (something happens) and must be followed by a full clause (with a finite verb):
- Ég klára heimavinnuna áður en ég fer að sofa.
  I finish my homework before I go to sleep.

So when you join two sentences (I finish my homework + I go to sleep), you need áður en, not just áður.

Why is the verb fer in the present tense if this is about a future action?

Icelandic (like English) often uses the present tense to talk about a future event, especially in:

time clauses with áður en, þegar (when), eftir að (after), etc.
things that are habitual, scheduled, or clearly in the future from context.

So:

Ég klára heimavinnuna áður en ég fer að sofa.
can mean: I finish / I’ll finish my homework before I go to sleep.

You could use the auxiliary mun for a clearer future:

Ég mun klára heimavinnuna áður en ég fer að sofa.
I will finish my homework before I go to sleep.

But it’s not required; the simple present is very natural here.

What does klára mean exactly, and is it the only way to say “finish”?

klára means to finish, to complete something. It’s very common and colloquial, used for:

klára matinn – finish the food
klára verkefnið – finish the assignment
klára bókina – finish the book

Other verbs that can mean finish include:

lúka (við) (more formal/literary):
- Ég lýk við heimavinnuna.
ljúka (við) (most common standard alternative):
- Ég lýk við heimavinnuna.

In everyday speech, klára is extremely frequent and perfectly natural in this sentence.

Why is it ég fer að sofa and not something like ég sef?

sofa = to sleep (infinitive).
ég sef = I sleep / I am sleeping (present of sofa).

The expression fara að + infinitive means roughly:

to be about to do something
to go and do something
often translated as go to [verb] or start to [verb].

So:

ég fer að sofa literally: I go to sleep / I’m about to sleep.
Ég klára heimavinnuna áður en ég sef is grammatically fine, but it sounds more like before I am (actually) sleeping.
Ég fer að sofa is the most natural way to express before I go to sleep as a routine or planned action.

What is the verb fara like? How is fer formed?

fara is an irregular verb meaning to go. Its present tense:

ég fer – I go
þú ferð – you (sg.) go
hann/hún/það fer – he/she/it goes
við förum – we go
þið farið – you (pl.) go
þeir/þær/þau fara – they go

Past tense:

ég fór – I went
þú fórst – you went
hann/hún/það fór – he/she/it went
við fórum – we went
þið fóruð – you (pl.) went
þeir/þær/þau fóru – they went

In the sentence, ég fer is just the normal present form I go.

Why is the word order Ég klára heimavinnuna and not something like Ég heimavinnuna klára?

Icelandic normally has verb-second (V2) word order in main clauses:

First position: usually the subject (here Ég).
Second position: the finite verb (here klára).
Then objects and other elements.

So:

Ég klára heimavinnuna. – subject (Ég) + verb (klára) + object (heimavinnuna).

You can move things around for emphasis:

Heimavinnuna klára ég fyrst. – The homework, I finish first.

But Ég heimavinnuna klára without a reason or extra context sounds odd and unidiomatic.

Why is heimavinnuna in the accusative case?

The accusative is most often used for the direct object of a verb.

Verb: klára (to finish)
What is being finished? → heimavinnuna (the homework) = direct object

So heimavinna must be in the accusative:

Nominative: heimavinnan – the homework (subject)
Accusative: heimavinnuna – the homework (object)

If heimavinna were the subject, it would be:

Heimavinnan er erfið. – The homework is hard. (nominative)

How would I negate this sentence? Where does ekki go?

To negate it, put ekki (not) after the verb in each clause:

Main clause: Ég klára ekki heimavinnuna …
Subordinate clause: … áður en ég fer ekki að sofa. (this would mean before I don’t go to sleep, which is odd in meaning, but grammatically shows the position)

A natural meaningful negative would be:

Ég klára ekki heimavinnuna áður en ég fer að sofa.
I don’t finish my homework before I go to sleep.

Structure:

Ég (subject)
klára (finite verb)
ekki (negation)
heimavinnuna (object)
áður en ég fer að sofa (time clause)

Is heimavinna always “homework,” or can it mean something else?

heimavinna usually means:

school homework / assignments to do at home.

Literally it is heim- (home) + vinna (work). In some broader contexts it can mean work done at home, like remote work, but in everyday speech it is strongly associated with school homework, just like in this sentence.

Is there any difference in meaning if I say Ég mun klára heimavinnuna áður en ég fer að sofa?

Yes, but it’s subtle:

Ég klára heimavinnuna áður en ég fer að sofa.
– Very natural, can describe a routine or a specific future plan. Context decides.
Ég mun klára heimavinnuna áður en ég fer að sofa.
– Emphasizes the future more clearly, similar to I will finish my homework before I go to sleep.
– Can sound a bit more determined / promised / planned.

Both are correct; the original present-tense version is the most neutral everyday phrasing.

How is áður en ég fer að sofa pronounced as a phrase? Do words run together?

Roughly (in a broad, learner-friendly transcription):

áður ≈ OW-thur (with Icelandic ð like the th in this).
en ≈ en.
ég ≈ yeh (often with a slight glide, not a hard “g”).
fer ≈ fehr (short e).
að ≈ a(th) (similar vowel to English father, with a soft ð).
sofa ≈ SO-va (stressed first syllable).

In fluent speech:

áður en tends to flow as one group: áðuren.
There is usually no strong pause between the words:
áður en ég fer að sofa is spoken quite smoothly, with the main stress on áður and sofa.