Ég tek með mér skilríkin þegar ég fer á flugvöllinn.

Taka is the infinitive (to take). In a normal present-tense sentence you conjugate it:

• ég tek = I take
• þú tekur = you take
• hann/hún/það tekur = he/she/it takes
  So Ég tek... is simply the correct present-tense form for ég.

taka með X is a very common Icelandic way to say take/bring along. So:

• Ég tek skilríkin með mér = I take/bring the ID with me (along).

It’s not just literal with; it’s an idiomatic “take along” construction that is extremely common in everyday speech.

On its own, the preposition með often goes with the accusative (e.g., með mig can occur). But in the set expression taka með sér (take along with oneself) the pronoun behaves like the “along-with” companion and is typically in the dative:

• með mér / með þér / með sér / með okkur / með ykkur / með sér

So með mér is the natural form in this “take along” pattern.

skilríki means ID / identification (document) and it’s very often treated as a neuter plural noun in real usage (like “papers” in English).
skilríkin = the ID / the identification documents (definite form).

The Icelandic definite article is usually attached as a suffix:

• skilríki = ID (indefinite)
• skilríkin = the ID (definite)

It is the direct object of tek, but with neuter plural nouns the nominative and accusative are identical. So:

• nominative plural: skilríkin
• accusative plural: skilríkin

That’s why you don’t see a visible change here, even though it’s functioning as an object.

In main clauses Icelandic is typically verb-second (V2) (the finite verb comes early). But after many subordinators like þegar (when), the clause is subordinate, and the usual order is:

• þegar + subject + verb ... So þegar ég fer... is the normal subordinate-clause word order.

flugvöllur = airport (masculine)
flugvöllinn = the airport in the accusative singular definite form.

Icelandic often marks the by adding a suffix, so instead of a separate word like “the,” you get endings like -inn.

This is a classic Icelandic case contrast:

• á + accusative often indicates movement to/toward a place
  
  • fara á flugvöllinn = go to the airport
• á + dative often indicates location at a place
  
  • vera á flugvellinum = be at the airport

So fer á flugvöllinn matches the idea of going there.

Often, yes, but there’s a nuance:

• þegar = when (especially a specific time/event: “when I go…”)
• er can also mean when/that, and is common in more general relative-type clauses.

In this sentence, þegar is very natural because it points to the specific situation “when I go to the airport.”

Icelandic usually doesn’t have a separate word like English the. Instead, the is commonly expressed by a suffix on the noun:

• skilríkin = the ID
• flugvöllinn = the airport