This might seem like a no-brainer, but READ the article before retweeting or sharing on a social media site. Make a call on the article before telling all your family and friends this is a must read.
Use websites such as Snopes or PolitiFact's Truth-O-Meter. Both of these sites are non-partisan and conduct careful research when deciding how true a statement was. There are other fact checkers out there as well, such as the one at the Washington-Post.
When an article cites a fact or figure, do they provide the source? You might have to do some digging to see if you can find their source.
When an article cites sources, it's good to check them out. Sometimes, official-sounding associations are really biased think tanks or represent only a fringe view of a large group of people.
Check the dates - information can have an expiration date. In many cases, use the most up-to-date information you can find.
Who's funding the organization that published the article? This can often impact/influence what is written. Some organizations are vocal about who does and does not fund them.
Remember that some articles are meant to be satire and not taken seriously. This includes The Onion.
Headlines: Headlines accurately represent the substance of articles, with minimally emotional language (recognizing that their purpose is as much marketing as informational).
Publication Credibility: The article is on a site published by an organization with a searchable identity and history, written by an author with a searchable identity and history, and conforms to a particular online genre of news publication (blog, citizen journalism, etc) or classic news genre (editorial, straight reporting, photo-essay, etc.)
Basic Facts: The basic information (who, what, when, where, why & how) is clear within the first few sentences, is supported with evidence, and can be confirmed in other news outlets.
Evidence: Articles consistently identify sources for information with names and/or links, and sources are credible, appropriate, and multiple. All reported facts, unless widely known, are verified with sources. It is also clear that reporting reflects skeptical pursuit of knowledge, not just relaying source information at face value. Facts are not cherry-picked to support a particular point.
Bias The publication is transparent about its publication and editorial processes: publication, funding, and editorial staff information is easily available, and editorial guidelines are clear and consistent. Biases are openly acknowledged, and retractions or corrections are issued when details are reported inaccurately.
A project of the Annenberg Public Policy Center of the University of Pennsylvania, factcheck.org primarily researches claims by politicians. Their processes and sources of funding are open and documented on their website.
PolitiFact fact-checks statements by politicians; they are the source of the fairly popular "Truth-O-Meter". It is run by editors and reporters from the Tampa Bay Times, an independent newspaper in Florida. Their funding and processes are documented on their website.