Learn Icelandic: Ég les bók.

In this sentence, bók is the direct object, which is the thing being read. Most action verbs like lesa (to read) force the noun receiving the action into the accusative case.

If bók is in the accusative case, why doesn't the spelling change?

Not all words change their spelling in the accusative case! For many feminine nouns like bók, the accusative form is exactly the same as the nominative (dictionary) form. You know it is in the accusative here because of its role in the sentence as the object.

Where is the word for "a" in this sentence?

Icelandic does not have an indefinite article like "a" or "an" in English. A bare, singular noun like bók naturally translates to "a book" in English.

Could Ég les also mean "I am reading a book"?

Yes! Icelandic doesn't use a separate "am doing" structure for the present tense like English does. Ég les covers both "I read" and "I am reading".