Við göngum yfir gangbrautina þegar umferðarljósið verður grænt.

Við can be either:

• the pronoun we
• or the preposition with / by / against, depending on context

Here it means we because it is followed by the finite verb göngum. In other words, við göngum is a complete subject + verb combination: we walk.

If við were a preposition, you would expect a noun phrase after it, not a finite verb.

Because göngum is the present-tense form that matches við = we.

The verb is ganga = to walk.
Its present tense changes by person and number:

• ég geng = I walk
• þú gengur = you walk
• við göngum = we walk

So ganga is the dictionary form, while göngum is the correct conjugated form for we.

In Icelandic, the definite article is usually attached to the end of the noun instead of written as a separate word.

So:

• gangbraut = crosswalk
• gangbrautin / gangbrautina = the crosswalk

and:

• umferðarljós = traffic light
• umferðarljósið = the traffic light

This is very normal in Icelandic. English uses a separate word the, but Icelandic usually adds it as a suffix.

Because gangbrautina is the definite accusative singular form of gangbraut.

Here is the idea:

• base noun: gangbraut = crosswalk
• definite: the crosswalk
• after yfir in this sentence, the noun is in the accusative

So gangbrautina means the crosswalk in the form required by the grammar of the sentence.

This is a very common thing in Icelandic: nouns change form depending on case.

Here yfir means across / over.

In this sentence, it describes movement across the crosswalk:
göngum yfir gangbrautina = walk across the crosswalk.

Many Icelandic prepositions can take different cases depending on meaning. With yfir:

• accusative often suggests movement across/over something
• dative often suggests position over/above something

So the accusative here makes sense because there is motion from one side to the other.

Þegar introduces a time clause and means when.

So the structure is:

• main clause: Við göngum yfir gangbrautina
• time clause: þegar umferðarljósið verður grænt

This is similar to English We walk across the crosswalk when the traffic light turns green.

Depending on context, þegar can sometimes feel close to when, once, or as soon as, but when is the basic meaning.

Because verða means become, and that fits a traffic light changing color.

So:

• verður grænt = becomes green / turns green
• er grænt = is green

For traffic lights, Icelandic very naturally uses verða where English often says turn:

• Ljósið verður grænt = the light turns green

So this sentence is describing a change of state, not just a static condition.

Because the adjective has to agree with umferðarljósið, which is neuter singular.

The adjective grænn = green changes form:

• grænn = masculine
• græn = feminine
• grænt = neuter

Since umferðarljósið is neuter, the correct form is grænt.

Also, after vera and verða, Icelandic uses a predicate adjective that agrees with the subject. So:

• ljósið verður grænt
• maðurinn verður þreyttur
• konan verður þreytt

Yes. Icelandic often uses the present tense for:

• general truths
• habits
• instructions
• near-future or expected future events

So this sentence can mean something like a general rule:
We walk across the crosswalk when the light turns green.

That is very natural. English does something similar too:

• We cross when the light turns green

So even though the event may happen in the future, the present tense is still normal.

The sentence has:

• a main clause first: Við göngum yfir gangbrautina
• then a subordinate clause: þegar umferðarljósið verður grænt

That is a normal order in Icelandic.

A useful thing to know is this: if you put the þegar clause first, the main clause changes word order because Icelandic main clauses are usually verb-second.

So you would say:

Þegar umferðarljósið verður grænt, göngum við yfir gangbrautina.

Notice that it becomes göngum við, not við göngum, after the fronted clause.

It is a compound noun:

• umferð = traffic
• ljós = light

So umferðarljós literally means traffic-light.

Icelandic uses compound words very heavily, much more than English in many cases.
Then the definite ending is added:

• umferðarljós = traffic light
• umferðarljósið = the traffic light

Even though a traffic light has multiple colored lights, the noun is singular here, just like English often says the light turns green.