Learn Icelandic: Jón prentar skjalið sitt. - Jón prints his own document.

Sitt is a reflexive pronoun, which means it points back to the subject of the sentence. Because Jón is printing his own document, we use sitt. If we said Jón prentar skjalið hans, it would mean Jón is printing some other man's document.

Since Jón is a man, why doesn't the pronoun take a masculine form like sinn?

Possessive pronouns like sinn must match the gender, number, and case of the thing being owned, not the owner. The word for document, skjal, is a neuter noun. Since Jón is printing it, it is the direct object (accusative case). The neuter, singular, accusative form of this pronoun is sitt.

Why does the noun have the attached 'the' ending (skjalið) if we already say 'his' (sitt)?

In English, saying 'the his document' sounds wrong. However, in Icelandic, it is the standard rule to add the definite article to a noun when it is followed by a possessive pronoun. So, skjalið sitt literally translates to 'the document his'.

Does the verb prenta force a specific case here?

Yes, prenta (to print) takes a direct object in the accusative case, just like most action verbs where you do something directly to an object. For a neuter word like skjal, the accusative form looks exactly the same as the nominative (dictionary) form.