Vejen til huset går gennem skoven.

Because Danish usually adds the definite article to the end of the noun.

• vej = road
• vejen = the road
• hus = house
• huset = the house
• skov = forest
• skoven = the forest

So English uses a separate word, but Danish often uses an ending instead.

Vejen is the definite singular form of vej.

Here the sentence is talking about a specific road, not just any road. So Danish uses vejen for the road.

• en vej = a road
• vejen = the road

Because huset means the house, and the sentence refers to a specific house.

The phrase til huset means to the house or, in this context, to the house as part of the road to the house.

If it were an unspecified house, you could say:

• til et hus = to a house

But til huset is definite: to the house.

Here til means to.

In vejen til huset, it connects road and house:
the road to the house

It is not showing movement in the sentence. It is part of the noun phrase describing which road we mean.

Yes. Vejen til huset is one noun phrase, meaning the road to the house.

You can think of it like this:

• main noun: vejen
• extra description: til huset

So til huset tells you which road.

In Danish, gå can be used about roads, paths, routes, lines, and similar things. In this kind of sentence, it means something like:

• go
• run
• lead

So Vejen til huset går gennem skoven is a natural Danish way to say that the road runs or goes through the forest.

Går is the present tense of gå.

• at gå = to go / to walk
• går = goes / is going

In this sentence it describes a general fact, so present tense is the normal choice.

Gennem means through.

So:

• gennem skoven = through the forest

This suggests the road passes from one side of the forest to another, or at least crosses it.

That is different from i skoven, which means in the forest.
I skoven only tells you location; gennem skoven tells you the road passes through it.

The basic order is:

subject + verb + prepositional phrase

So:

• Vejen til huset = subject
• går = verb
• gennem skoven = prepositional phrase

This is standard Danish main-clause word order.

It depends on the grammatical gender of the noun.

• Common gender nouns usually take -en
• Neuter nouns usually take -et

In this sentence:

• en vej → vejen
• et hus → huset
• en skov → skoven

So you need to learn each noun together with its article: en or et.

Yes, often you can. Gennem and igennem are very close in meaning, and in many sentences both are possible.

Here, går gennem skoven is completely natural.
Går igennem skoven would also be understandable, but gennem is very common and simple in this kind of sentence.

A rough guide is VY-en, where vy rhymes loosely with English my, but with a Danish-style v sound.

A few helpful pronunciation notes for the whole sentence:

• vejen: roughly VY-en
• huset: roughly HOO-set
• går: a bit like gor, but with a more open Danish vowel
• gennem: roughly GEN-em
• skoven: roughly SKOH-ven

The real Danish pronunciation is softer and less exact than English spelling suggests, so it is best to listen to native audio if possible.