Learn Polish: Nie czytam artykułu. - I am not reading the article.

Because of the word nie. The verb czytać normally takes the Accusative case for its direct object. For example, if you say 'I am reading the article', it is Czytam artykuł. However, when you negate a verb that usually takes the Accusative, the object changes to the Genitive case. This is called the Genitive of negation.

Why does the Genitive form of artykuł end in -u instead of -a?

Artykuł is a masculine inanimate noun (a thing, not a person or animal). In the Genitive case, these nouns can end in either -a or -u. There is no single strict rule, but many abstract nouns, foreign loanwords, and objects like artykuł take the -u ending. You often just have to memorize which ending a masculine inanimate noun uses.

Why is there no Polish word for 'I' in this sentence?

In Polish, the verb ending usually tells you exactly who is doing the action. The -m ending on czytam already means 'I am reading'. Adding the pronoun ja is unnecessary unless you want to emphasize it, for example, to say that you are not reading the article, but someone else is.

Does nie always go right before the verb?