Amióta köd van, a turistajelzéseket keressük.

Here amióta introduces a time clause and means since, ever since, or from the time when.

So:

Amióta köd van, ... = Since there is fog, ... / Ever since it became foggy, ...

A very common contrast is:

• Mióta? = Since when?
• Amióta ... = Since ...

So mióta is often a question word, while amióta is often used to connect a clause.

Hungarian often expresses weather or surrounding conditions with a noun plus van.

So:

• köd van = literally there is fog
• natural English translation: it is foggy / there is fog

Hungarian does not need a dummy subject like English it in weather expressions. So instead of saying something like it is foggy, Hungarian commonly says fog is present.

Because köd here is being used in a general, uncountable sense: there is fog.

So köd van is the normal way to say:

• there is fog
• it is foggy

Using a köd would mean the fog, referring to some specific fog already identified in the conversation, and that would usually not sound natural in this kind of weather statement.

This is a very important difference between English and Hungarian.

Hungarian often uses the present tense for an action or situation that started in the past and is still continuing now, especially with words like amióta.

So:

• Amióta köd van, a turistajelzéseket keressük.

can naturally correspond to English:

• Since it got foggy, we have been looking for the trail markers.

Even though English prefers the present perfect or present perfect continuous, Hungarian often simply uses the present.

Turistajelzéseket is built from several parts:

• turista = tourist
• jelzés = sign, marking, signal
• turistajelzés = tourist trail marking / trail sign / trail blaze
• -ek = plural
• -et = accusative ending for the direct object

So turistajelzéseket means trail markers, tourist trail signs, or trail blazes as a direct object.

Hungarian often builds long words by combining:

• a compound noun,
• a plural ending,
• and a case ending.

Because the object is definite.

• a turistajelzéseket = the trail markers

This suggests that the speaker has specific markers in mind, for example the route markers they expect to find on a hiking trail.

That definite object also affects the verb form, which is why the verb is keressük and not keresünk.

Because Hungarian verbs have two main conjugation patterns:

• indefinite conjugation
• definite conjugation

Here the object is definite:

• a turistajelzéseket = the trail markers

So Hungarian uses the definite verb form:

• keressük = we are looking for it/them

Compare:

• Turistajelzéseket keresünk. = We are looking for trail markers.
  (not specific ones; indefinite)

• A turistajelzéseket keressük. = We are looking for the trail markers.
  (specific ones; definite)

It is not stated separately because Hungarian verbs usually already show the subject.

Keressük tells you that the subject is we, and also that the verb is in the definite conjugation.

So Hungarian does not need mi here.

• keressük = we are looking for it/them

You could add mi for emphasis, but normally it is left out:

• Mi keressük a turistajelzéseket. = We are the ones looking for the trail markers.

Hungarian word order is much more flexible than English word order. It is not based mainly on subject-verb-object order, but on topic and focus.

In this sentence:

• a turistajelzéseket comes before the verb because it is the thing being talked about, the topic.

So the sentence is structured more like:

• As for the trail markers, we are looking for them.

This does not mean the sentence is especially dramatic or strange; it is a normal Hungarian pattern.

A different word order can be possible too, but it may shift the emphasis.

Because Hungarian keres works differently from English look for.

In English:

• look for uses the preposition for

In Hungarian:

• keres takes a direct object in the accusative

So Hungarian says, literally:

• we search the trail markers

But the natural English translation is:

• we are looking for the trail markers

This is a common thing to watch out for: Hungarian and English often use different grammar even when the meaning is the same.

Because Amióta köd van is a subordinate clause placed before the main clause.

So the sentence has two parts:

• Amióta köd van = subordinate time clause
• a turistajelzéseket keressük = main clause

Hungarian normally separates this kind of clause with a comma, just as English often does:

• Since there is fog, we are looking for the trail markers.

So the comma is standard punctuation here.