Have a conversation. Get out your pen, and start to scribble on the paper.
Ask some questions. Here's a common list:
(1) What kind (genre) of journalism is it?
(2) What kind of occurrence or event produced the news story?
(3) Why is this story in the paper?
(4) Was this event created in order to get coverage?
(5) What is the writer's background? (if none is given, assume none)
(6) Is there obvious bias on the part of the writer of the article (or the writer of the headline)?
(7) Is it possible to verify the information in the article? (Are there other papers covering it? What do they say?)
(8) What sources are used in the newspaper article? Are some apparently made up?
(9) What kind of play is given to the story?
(10) What is omitted or left out?
(11) How is the event framed? Is there a "larger story" we are supposed to infer? If so, did this story distort the reporting?
(12) What are the "latent" values being transmitted by the news articles?
Like many people my age, I have seen the newspapers cover events that I have been part of: I have never been able to think that they did a good job when I know about the event myself. That same thought should be applied to their coverage of other events. I have particularly come to recognize that words used to characterize people are rarely useful, and are usually actively misleading: "conservative" "liberal" "fundamentalist" come to mind as words which are almost invariably misapplied or used to conceal, rather than reveal, the truth. Some newspapers recognize, at least implicitly, that they are losing readers, (sometimes noticing it), and want to make a joke of it. A few of us notice that certain papers will report well, and switch to them.
Finally, for those interested in evaluating the reasoning of an article or editorial, I recommend this.