Learn Icelandic: Hann var þriðji strákurinn í dag.

Ordinal numbers like "first", "second", and "third" behave like weak adjectives in Icelandic. Because strákurinn (the boy) is a masculine noun in the nominative case, þriðji takes the masculine weak ending -i. If it were a feminine noun like stelpan (the girl), it would be þriðja.

Why does strákurinn have the "the" ending (-inn) attached if there is no separate word for "the" before "third"?

In Icelandic, when you use an ordinal number like þriðji, the noun that follows it usually takes the definite article attached to its end. The phrase naturally translates to "the third boy" in English, even without a separate word for "the" in the Icelandic sentence.

Why doesn't the word for "boy" change to the accusative case after the verb?

Because the verb is var (was). The verb að vera (to be) works like an equals sign linking "He" and "the third boy". Both sides of this "equation" describe the same thing, so they both stay in the nominative case.

Does í dag literally translate to "in day"?

Yes! Icelandic uses the preposition í (in) plus dag (day) as a fixed phrase to mean "today".