Learn Icelandic: Strákurinn gengur á fjallið. - The boy walks up the mountain.

The preposition á usually means "on" or "onto". When you walk "onto" a tall geographical feature like a mountain (fjall), we usually say "up" in English. He is moving from off the mountain to on it.

Is fjallið in the accusative case here?

Yes! This sentence uses á to show motion towards a destination. Because the boy is moving onto the mountain, á forces the noun into the accusative case. If he was already up there walking around, á would take the dative case instead.

If fjallið is accusative, why does it look exactly like the standard dictionary form?

Fjall (mountain) is a neuter noun. A very helpful rule in Icelandic is that all neuter nouns look exactly the same in the nominative (subject) and accusative cases. The attached word for "the" (-ið) also stays exactly the same.

How do the endings on strákurinn and fjallið work again?

This is the Icelandic definite article (the word for "the"), which attaches directly to the end of the noun rather than being a separate word. Strákur (boy) is masculine and takes the ending -inn. Fjall (mountain) is neuter and takes -ið.