Learn Icelandic: Nemendurnir lesa bókina saman. - The students read the book together.

The base word is nemandi (student), which belongs to a special group of masculine nouns ending in -andi. In the plural, the vowel changes and they take the ending -endur, making it nemendur. When you add the masculine plural definite article -nir, you get nemendurnir.

Why is the book written as bókina here instead of bókin?

The verb lesa (to read) takes a direct object in the accusative case. The word bók (book) is a feminine noun. While its nominative (subject) form with the definite article is bókin, the accusative definite form changes to bókina.

Could I use með instead of saman to say they read together?

No, because með means with and requires an object to follow it, for example if you said they read with the teacher (með kennaranum). When you just want to express that people are doing an action jointly without naming another party, you must use the adverb saman (together).

Does lesa mean they are reading right now, or that they generally read?

It can be both! Icelandic does not have a separate continuous tense like English does. Depending on the context, lesa can mean they are actively reading it right now, they read it regularly as a habit, or even that they will read it in the future.