"We read them a newspaper."
Translation:Noi leggiamo loro un giornale.
Leggere is a transitive verb, accepting a direct object corresponding to "what is being read". It also accepts indirect objects ("to whom"). Italian syntax would normally be: verb + direct object pronoun + indirect object pronoun. In this sentence, "a newspaper" is the direct object noun, and "them" is the indirect object pronoun. We can construct this sentence two ways: "We (to them) read (a newspaper)." OR "We read (a newspaper) (to them)." English grammar would only accept the latter as proper. The reason loro comes after the verb, is because loro is the exception. This is correct, as well as "Noi leggiamo un giornale a loro." The added "a" clarified to whom the action is directed.
As an example, if the English example was: "We read her a newspaper" the translation would be "Le noi leggiamo un giornale." or "Noi leggiamo un giornale a le."