Learn Icelandic: Strákurinn gengur upp úr kjallaranum. - The boy walks up out of the basement.

The preposition úr specifically means moving out of a contained space, like a room, a box, or in this case, a basement. If you used frá, it would just mean moving away from the general area of the basement, not actually exiting the inside of it.

Does úr always trigger the dative case?

Yes, úr always forces the noun that follows it into the dative case. That is why we see the dative form of the word for basement here.

How is the word kjallaranum formed?

The basic dictionary word is the masculine noun kjallari (basement). In the dative case, it drops the final i and becomes kjallara. To say 'the basement', we add the dative masculine definite article -num, giving us kjallaranum.

Why is the directional word upp used here instead of uppi?

In Icelandic, many direction words have two forms: one for movement and one for standing still. Because the boy is actively walking upward out of the basement, we use upp. If he were just standing still upstairs, we would use uppi.