Learn Icelandic: Hann kaupir rauðan bíl.

Because it is describing bíl (car), which is a masculine noun. In this sentence, the car is the direct object (the thing being bought), so it is in the accusative case. Masculine adjectives in the accusative case take the strong ending -an.

Wait, isn't the dictionary word for car bíll with two L's? Why is it just bíl here?

Yes, the dictionary form (nominative case) is bíll. But because the car is the direct object receiving the action of the verb kaupir, it changes to the accusative case. For this specific masculine noun, the accusative form drops the second L, becoming bíl.

How do I know if kaupir means 'buys' or 'is buying'?

You can only tell from context! Icelandic doesn't have a separate '-ing' tense (present continuous) like English does. The single present tense form kaupir translates to both 'buys' and 'is buying' depending on what makes the most sense in the conversation.

Would the adjective ending change if he was buying a feminine object, like a book (bók)?

Exactly! Because bók is a feminine noun, you would use the feminine accusative strong ending -a, making it rauða bók. If it were a neuter noun like epli (apple), it would take the -t ending, becoming rautt epli (the spelling changes slightly from rauðt to rautt).