Learn Icelandic: Hann stakk blaðinu í vasann. - He stuck the paper in the pocket.

The verb stinga (to stick, put, or thrust) dictates the case of its object. When you stick or insert something, that object takes the dative case. Here, the word blað becomes the dative definite blaðinu.

If blaðinu is dative, why is vasann in the accusative case?

The case of vasann (the pocket) is controlled by the preposition í. Because the sentence describes movement into a destination (putting the paper into the pocket), í triggers the accusative case. If the paper were just resting inside the pocket, you would use the dative case instead.

In English we say 'in his pocket', but the Icelandic sentence says 'in the pocket' (í vasann). Is this typical?

Yes! In Icelandic, when talking about body parts or personal items like clothing where the owner is obvious from the context, you typically just use the definite article (the suffix -nn) rather than a possessive pronoun like hans.

Could I use the verb setja (to put) instead of stinga here?

You could, but stinga is much more natural for this specific action. Stinga is the go-to verb for sliding or inserting something into a confined space, like a pocket, an envelope, or a slot. Setja is more general, like placing an object onto a table.