"She does not read letters."
Translation:Hon läser inte brev.
The verb always needs to go in the second place, but inte comes between the verb and objects, and even between the verb and the particle as in tycker om or any prepositions. Other adverbs may come between the verb and inte if they modify the whole sentence, like Han läser faktiskt inte brev, 'He is actually not reading letters'.
The word order is different for main clauses and dependent clauses. In a main clause it is as Arnauti describes but in a dependet clause the "inte" and other adverbs are put between the subject and the verb.
For example: "I know that she doesn't read letters" "Jag vet att hon inte läser brev".
"I am sad because he doesn't like apples" "Jag är ledsen eftersom han inte tycker om äpplen"
Subject - Verb - Adverb - Object" is the most frequent word order in main clauses, but there's no rule saying that you need to structure them that way – the rule only says you must have the verb second. So you can just as well have Adverb-Verb-Subject-Object or even Object-Verb-Subject-Adverb.