Learn Icelandic: Hann tekur diskana af hillunum. - He takes the plates off the shelves.

Hillunum means "the shelves". It is in the dative case because it follows the preposition af (off/from). Because it is plural and definite (meaning it includes "the"), it takes the definite dative plural ending -unum.

Does the preposition af always make the next word dative?

Yes! The preposition af always forces the noun that follows it into the dative case. That is why the sentence uses the dative hillunum instead of the nominative hillurnar (the shelves).

Why is it diskana instead of diskar or diskarnir?

Diskana is the direct object of the verb tekur (takes), which means it must be in the accusative case. Diskur (plate) is a masculine noun. When you make it plural and add the definite article ("the"), the accusative form becomes diskana (the plates).

The dictionary form of the verb is taka. Why does it change to tekur here?

Many Icelandic verbs have a vowel shift when they are conjugated. For taka, the a changes to an e in the singular forms (I, you, he/she/it). Because the subject is hann (he), the correct form is tekur.