Steps in Summary:
1. Read, watch or listen carefully to the news story.
2. Determine whether it is a news report or an opinion piece.
3. Analyze the sources cited in the news story.
4. Gather and compare several news stories from the same agency over time.
5. Gather and compare news stories from different news agencies.
Read, watch or listen to the story carefully. Does the reporter use language that is inflammatory? Does the language tend to favor one side over another?
This page on news bias from the University of Michigan highlights numerous examples of bias evidenced by word choice: News Bias Explored: Word Choice
How is the story "framed"? In other words, is the story placed within a larger context? Is the issue or event presented as part of a larger trend? If so, notice whether the story "frame" makes the story seem more sensational, or reveals cultural or other types of bias.
Here's an example of story framing from a commentary in The Atlantic magazine: 'Framing' a Story: Journalism 101
Detecting bias may require you to look at a series of articles over time. Is the news agency reporting certain stories over others? Bias by selection is commonly related to:
This article from CBSnews.com describes an example related to covering kidnappings in the media: A Tale of Two Kidnappings
Analyze the sources used by the reporter. Some reporting can be biased if it is based on sources that have a strong, one-sided bias. Of course, all sources have bias, but the key idea here is that this reporting is based on a single viewpoint instead of many viewpoints.
This 2003 study from the watchdog organization FAIR (Fairness and Accuracy in Reporting) reports on biased sources used by American news media collectively in their coverage of the Iraq War: Amplifying Officials, Squelching Dissent
Newspapers and news agencies frequently provide a platform for individual opinions in the form of editorials, letters to the editor, columns and commentaries. It can sometimes be tricky to tell the difference between an opinion piece and a news report:
Note that the author is taking a stand on this issue, calling it a dumb idea. Read carefully and you'll note that this is the author's voice, not someone's opinion that he is quoting. In some opinion pieces the author may also refer to himself or herself as "I".
Here's a news article on the same issue. Notice that the reporter does not make her own judgment on the issue; all opinions expressed in the article are attributed to someone else.
To detect bias by omission, you need to check other sources and compare the reporting -- or have first-hand knowledge of the issue. Has the report left out certain facts or viewpoints, creating an unbalanced representation of the issue?
Here's an example of bias by omission from a news bias site at the University of Michigan: