Learn Icelandic: Mig langar að lesa blöð.

The verb langa (to want) is what is called an impersonal verb. It requires the person having the feeling to be in the accusative case. So, instead of the regular subject Ég (I), you must use the accusative pronoun Mig (me). It translates literally to something like 'It longs me.'

Why is the word for newspapers blöð instead of blað?

blöð is the plural form of the neuter noun blað (paper or newspaper). The verb lesa (to read) requires its object to be in the accusative case, so we need the accusative plural here. For neuter nouns, the accusative plural is exactly the same as the nominative plural. Notice how the vowel changes from a to ö in the plural—this is a very common vowel shift in Icelandic!

How would I say 'I want to read THE newspapers' using the definite form?

You would add the definite plural suffix to make it blöðin (the newspapers). In this sentence, we just use the bare plural blöð because the speaker wants to read newspapers in general, rather than specific ones.

What does að do in this sentence?

að is the infinitive marker, acting exactly like the word 'to' in the English phrase 'to read'. You use it to connect the main verb (langar) with the action the person wants to do (lesa).