Learn Hardcore Icelandic: Hún vill taka þátt í kvöldgöngunni. - She wants to take part in the evening walk.

Hún – personal pronoun, 3rd person singular feminine, nominative. It is the subject of the sentence (the one who wants something).
vill – 3rd person singular present of the verb vilja (to want). This is the main (finite) verb.
taka – infinitive of taka (to take). It is the infinitive complement of vill.
þátt – accusative singular of the noun þáttur (a part, share). It is the direct object of taka in the fixed expression taka þátt.
í – preposition í (in). It governs the dative here.
kvöldgöngunni – dative singular definite of kvöldganga (evening walk). This is the object of the preposition í and means in the evening walk.

So structurally:
[Subject] Hún + [modal] vill + [infinitive phrase] taka þátt + [prepositional phrase] í kvöldgöngunni.

Why is there no word like to before taka, when in English we say wants to take?

In Icelandic, an infinitive verb does not need a separate word like English to.

The form taka itself is the infinitive (the “to take” form).
After certain verbs, especially verbs like vilja (want), geta (can), skula (shall), mega (may), ætla (intend), the infinitive usually comes directly without að (the word that often corresponds to English to, as in að borða – to eat).

So:

Hún vill taka þátt
literally: She wants take part (no extra word needed)

Adding að here (Hún vill að taka þátt) is ungrammatical. With vilja, the pattern is simply:

[Subject] + vill + [infinitive]
Hún vill taka… / Við viljum fara… / Þeir vilja borða…

Is taka þátt one verb, and what does it literally and idiomatically mean?

taka þátt is not a single verb but a verb–noun expression:

taka – the verb to take
þátt – the noun þáttur (a part, share) in the accusative singular (object of taka)

Literally, taka þátt means to take a part.

Idiomatically, it corresponds to to take part, to participate.
So taka þátt í e-u means:

taka þátt í
- dative = take part in something, participate in something

It behaves like an idiom; you don’t normally split it or replace þátt with another word. The common pattern is:

taka þátt í keppninni – take part in the competition
taka þátt í verkefninu – take part in the project
taka þátt í kvöldgöngunni – take part in the evening walk

What is þátt exactly – what is its base form and case, and why is it in that form?

The base noun is þáttur (masculine), meaning part, share, segment (also used for episode of a TV show).

Its main singular forms:

Nominative: þáttur – (a) part (as subject)
Accusative: þátt – (a) part (as object)
Dative: þætti
Genitive: þáttar

In taka þátt, þátt is in the accusative singular, because it is the direct object of taka:

taka (take) + þátt (a part, accusative) → taka þátt (take part)

You basically always see it as þátt in this expression, because it is always being “taken” as an object.

Why is it í kvöldgöngunni (dative) and not í kvöldgönguna (accusative)?

The preposition í can take either dative or accusative, depending on the meaning:

í + dative → location / being inside / in something
(where? in what?)
í + accusative → movement into / going into
(into where? into what?)

Examples:

Hann er í húsinu. – He is in the house. (dative, location)
Hann fer í húsið. – He goes into the house. (accusative, motion)

In taka þátt í kvöldgöngunni:

You are participating in an event, not moving into it.
It is about being in the context of the walk, not going into the walk as a physical space.

So í takes the dative, giving í kvöldgöngunni (in the evening walk).

If you said í kvöldgönguna, that would suggest motion into the walk (as if you are walking into it), which is not how taka þátt í works.

What does the ending -unni in kvöldgöngunni tell me?

kvöldgöngunni contains several pieces of information at once:

The base noun is kvöldganga (evening walk), which is:
- feminine
- a weak -a noun
The root changes because of u-umlaut:
- ganga → göngu in oblique cases (acc/dat/gen)
  so kvöldganga → kvöldgöngu in those cases.
The ending -unni signals:
- dative singular
- definite (the)

So:

kvöldganga – an evening walk (nominative, indefinite)
kvöldgangan – the evening walk (nominative, definite)
kvöldgöngu – (to/at/in) an evening walk (dat/acc/gen, indefinite)
kvöldgöngunni – (to/at/in) the evening walk (dative singular definite)

Thus kvöldgöngunni specifically means in the evening walk, not just “in an evening walk” and not plural.

How would the sentence change if I wanted to say an evening walk or evening walks instead of the evening walk?

You mainly need to change the noun phrase after í.

an evening walk (indefinite, singular)
After í with a locative meaning, we need dative singular indefinite:
- í kvöldgöngu – in an evening walk
Full sentence:
- Hún vill taka þátt í kvöldgöngu.
  – She wants to take part in an evening walk.
evening walks (plural)
Dative plural of kvöldganga is kvöldgöngum (indefinite):
- í kvöldgöngum – in evening walks
Full sentence:
- Hún vill taka þátt í kvöldgöngum.
  – She wants to take part in evening walks.
the evening walks (definite plural)
Dative plural definite adds -unum:
- í kvöldgöngunum – in the evening walks
Full sentence:
- Hún vill taka þátt í kvöldgöngunum.
  – She wants to take part in the evening walks.

Can I also say this with langar, and what is the difference between vilja and langar?

Yes, you can express the idea with langar, but the structure changes.

With vilja (our original sentence)
- Hún vill taka þátt í kvöldgöngunni.
  – She wants to take part in the evening walk.
vilja behaves like a normal verb:
[subject in nominative] + vilja + infinitive
With langar
langar is impersonal and works differently:
- The person who has the desire is not the subject, but an object (usually in accusative).
- The subject is a dummy það (often omitted in speech and writing).
Pattern:
- (Það) langar hana til að taka þátt í kvöldgöngunni.
  literally: It longs her to take part in the evening walk.
More natural Icelandic would be:
- Hana langar til að taka þátt í kvöldgöngunni.
Differences:
- Hún vill… – more straightforward wants to, a bit more direct and volitional.
- Hana langar… – feels like, would like to, more about desire/longing, often slightly softer in tone.

Both are correct; you just have to respect their different grammar patterns.

How do I put this sentence into the past or (simple) future?

Past tense – “She wanted to take part…”
Use vildi (past of vilja):
- Hún vildi taka þátt í kvöldgöngunni.
  – She wanted to take part in the evening walk.
Future meaning – “She will want / is going to want to take part…”
Icelandic often uses the present tense for near future, so the original:
- Hún vill taka þátt í kvöldgöngunni.
can already mean She wants to (is going to) take part in a future walk.
If you really want a clear future auxiliary, you might say:
- Hún mun vilja taka þátt í kvöldgöngunni.
  – She will want to take part in the evening walk.
But this literally means “will want”, which is a bit different in nuance from English “will take part” (it focuses on wanting, not on the actual participation).
To talk about definitely taking part, Icelanders might say something like:
- Hún ætlar að taka þátt í kvöldgöngunni.
  – She is going to take part in the evening walk. (plans/intends to)

Can I move í kvöldgöngunni to another place in the sentence, or is the word order fixed?

Word order in Icelandic is fairly flexible, but there are natural preferences.

The most neutral, idiomatic version is:

Hún vill taka þátt í kvöldgöngunni.

You can move the prepositional phrase í kvöldgöngunni for emphasis or style:

Fronting the prepositional phrase (emphasis on where/in what she participates):
- Í kvöldgöngunni vill hún taka þátt.
  – In the evening walk, she wants to take part.

This is grammatical and natural when you want to highlight the evening walk.

What you generally don’t do is split the idiom taka þátt í in an odd way, e.g.:

Hún vill í kvöldgöngunni taka þátt. – grammatical but sounds awkward; the idiom feels better kept together as taka þátt í X.

So yes, you can move í kvöldgöngunni, but the default and most natural order is the one you saw first.

How do I pronounce the tricky parts of Hún vill taka þátt í kvöldgöngunni?

Very rough English approximations (not precise phonetics):

Hún – roughly like hoon (long ú like “oo” in food).
vill – roughly like vitl:
- ll is often pronounced like tl (with a little puff of air), not like English l.
taka – TAH-ka:
- a is more like the a in father.
þátt – roughly thout:
- þ is like th in think (never like th in this).
- á is a diphthong, a bit like the ow in now.
- final tt often sounds close to ht here, so somewhere between thaut and thout.
í – like a long ee in see.
kvöldgöngunni – in three chunks:
- kvöld – like kveld, with a short e (and a little d sound at the end).
- göng- – gung but with the vowel like German ö (a bit like eu in French feu).
- -unni – roughly -unny (short u like in pull, not fun).

Put together slowly:
Hún vill taka þátt í kvöldgöngunni → hoon vitl TAH-ka thout ee KVELD-gung-unny (very approximate).