Learn Hardcore Icelandic: Ég leita að lykli.

leita að is a verb-plus-preposition construction meaning “to look for” or “to search for.” You cannot use leita alone to express “looking for” in Icelandic.

Why is lykli in the dative case?

The preposition að always governs the dative. The base form lykill (nominative) becomes lykli in the dative to match að.

Can I omit að and say Ég leita lykli?

No. leita must be paired with að to have the meaning “look for.” Omitting að results in an ungrammatical phrase.

How do I say “I’m looking for the key” (definite) instead of “a key”?

Attach the definite ending to lykill before putting it in the dative. You get lykillinn → dative lyklinum. So the sentence is:
Ég leita að lyklinum.

Why isn’t there a word for “a” before lykli?

Icelandic does not use a separate indefinite article. A bare noun without a definite ending is understood as “a/an.”

How do I express the ongoing action “I’m looking for…” more explicitly?

Use the continuous-periphrastic construction vera að + infinitive.
Eg. Ég er að leita að lykli.
This emphasizes that you are in the process of searching right now.

What’s the difference between leita að and finna?

leita að = “to look for,” describing the act of searching
finna = “to find,” describing the act of discovering or locating something
After searching, you might say: Ég fann lykilinn (“I found the key”).

How do you pronounce Ég leita að lykli?

Approximate English pronunciation:
YEHG LAY-tah ath LIK-lee
In IPA roughly: /jɛːɣ ˈleiːta at ˈlɪcːi/.

How would I turn it into a question like “Are you looking for a key?”

In Icelandic you invert verb and subject:
Ertu að leita að lykli?
Or more simply (using simple present):
Leitarðu að lykli?