Learn German: Er liest morgens die Zeitung. - He reads the newspaper in the morning.

The infinitive verb meaning to read is lesen. It is a strong verb that changes its stem vowel from e to ie in the du (you) and er/sie/es (he/she/it) forms. Because of this rule, you do not say er lest, but rather er liest.

Why does morgens have an s at the end?

Adding an s to a time of day and making it lowercase turns it into an adverb that describes a regular habit. Der Morgen is the noun for the morning, but morgens means in the mornings or every morning.

Could I put morgens at the very end of the sentence, like in English?

It is much more natural to put it where it is. In German sentences, time words usually come before the object. A good rule of thumb to remember is Time before Object. So, the time (morgens) comes right after the verb and before the thing being read (die Zeitung).

Why is it die Zeitung if it is the direct object? Doesn't the word for the change in the accusative case?

It only changes for masculine nouns (where der becomes den). Zeitung is a feminine noun, and feminine nouns use die for both the subject (nominative case) and the direct object (accusative case). So it stays exactly the same!