Fact checking through citation 
The fact checking process at a standard US magazine (in the US at least, newspapers are not usually fact-checked) consists of ensuring statements in an article are appropriately derived from physical records. For example, a statement like "'Elephants eat potatoes frequently,' Franklin campaign spokesman Robert Torgnot said." is checked against a source like:
- the reporter's contemporaneous notes
- an audio recording of the reporter's conversation with Mr. Torgnot
- a published transcript of a press conference with Mr. Torgnot
In the standard process, the facts are simply verified against the sources and the article is published. After all, in the standard magazine it hardly seems appropriate to do much more, like including footnotes for each statement, especially when most would point to things (like the reporter's personal notes) that are rather difficult for the reader to obtain.
But with Wikinews we have a golden opportunity to do something different: we can publish all the source material and include links for each statement to the specific place where a claim can be verified. Reporters' notes may be scanned in; audio conversations may digitized. The reader need no longer take the publication's word that such statements are true; they can verify it for themselves. Worried that a quote may have been taken out of context? Listen to the whole conversation to get the context. And so on. Wikinews can afford to do this since it is not limited by the space constraints of the typical magazine.
Documenting such things will certainly take some extra work. However, considering the credibility problems a newly-started collaboratively-edited Internet-based news source is likely to have, the time will be well-spent. Furthermore, the additional information will be invaluable to researchers, television or radio news producers (who might include audio clips in a television show), and others who make use of Wikinews.
Types of reporting 
Unlike Wikipedia, Wikinews will be a primary information source. That means that the project will present original material, and report new information, not just compile and summarize information found elsewhere.
Of course, anyone, including anonymous users, can summarize reports from external sources, provided that they cite the source. But questions arise about how to treat original reporting.
Plan 1: Accredit reporters 
Accredited Wikinews reporters are users who are trusted by the community, who have actively participated in the project for some time (by copyediting, summarizing external sources, participating in discussions, reporting facts through an accredited Wikinews reporter etc.), and who have revealed their identity. Their real name has to be public, and their identity should be verified by another Wikinews reporter. The process of accreditation will therefore be similar to the process of applying for adminship on many Wikipedias.
Accreditation would be a binary thing: You're either accredited, or you aren't. There is no hierarchy in which you can advance step by step.
Facts and observations reported by Wikinews reporters would be usually phrased like: "According to Wikinews reporter Erik Möller, the three-headed monkey then jumped up and down, threatening to kill the villagers."
Accredited reporters could also, in effect, vouch for the trustworthiness of other (including anonymous) witnesses, allowing their reports to be published. Other named witnesses could have their reports published if there was a consensus among reporters that their report was credible.
Aren't you violating wiki principles with those accredited reporter restrictions?
If we are, then so is Wikipedia, because it does not allow any original research. Wikinews could be like Wikipedia, and just allow people to summarize external sources. That would work, but it would be a lot less interesting than having a world-wide team of wiki-reporters looking for stories to write about. This makes Wikinews actually more open than Wikipedia, but because of the need for immediate reliability of Wikinews reports, some restrictions have to be in place.
Why not just allow any named person to report anything, and require consensus for inclusion?
The accredition process allows for information that is harmful to, say, a certain politician or political party to be included regardless of whether other people like it or not: Wikinews reporters gain a level of independence that cannot be granted to everyone because that would result in a giant rumor-mill. The above proposal does what you suggest, and then expands the scope of reporting a little more through the concept of accredited reporters.
Plan 2: Reporter profiles 
Another way to deal with the credibility and bias of individual reporter is to give each reporter a "profile" and/or a "feedback" page. This would be in addition to traditional Wikimedia user pages, and would serve as a place for others to compile evaluations of a reporter's work and information about their background. This page will be easilly accessible from any story to which the reporter has contributed, and will allow the interested reader to learn about the source of their news.
This way, we don't pretend that individual reporters are unbiased and that every reporter is credible. Instead, we put everything in the open, and give our readers the ability to evaluate for themselves.
This could be implemented in place of accreditation or in addition to it, and would serve a useful purpose in either case.
Implementation plan 
Phase 1 
Phase 1 will require no changes to the software. Stories will be worked on in a "Workspace:" namespace. Once they are ready to be published, they will be tagged with a "Category:Ready for publication". These stories will then undergo systematic review for another period of time, in which the editors try to find consensus.
If there is consensus, Wikinews reporters will manually update the Main Page (or a separate page for less important stories) with the latest stories in the different categories, as soon as the stories are published. After publication, stories will be protected, and edits will be made only for updates.
Phase 2 
Phase 2 will require a special kind of macro to dynamically show the first paragraph of the n latest articles in a category. This will make it possible to have the Main Page and other news overview pages updated automatically based on the content of the categories. It will also make it easy to maintain separate pages for minor stories which do not show up on the Main Page. RSS feeds for this would be nice, but are not necessary.
The act of tagging an article with a category will be equivalent to publishing it.
Phase 3 
Phase 3 will use Wikiflow to move articles from one stage into the next: As soon as there is consensus, an article will flow into the published state, which will be evaluated by the category feed system described above, and can also be used to generate standard headers for articles which are not yet published ("This article is a work in progress ...."). Wikiflow will also soften page protection and thereby reduce the dependency on sysops to make minor updates.
Content transclusion from and to Wikipedia and other Wikimedia wikis would be desirable in this stage.
We should evaluate how other "citizen journalism" or grassroots journalism efforts have formed, and to learn from their successes and mistakes.
Some people claim that Indymedia is clearly a political advocacy site, just as some claim that Wikipedia is a political advocacy site. Others point out that No it is not. It is a news site that happens to have many a supporter and writer with a political leaning to the left. Many would be somewhat affronted by the assertion that it is a 'political advocacy site'. That the exposition of the truth tends to give strength to 'left wing' points of view only means that said left wing point of view does tend to be based on accurate observations. Editorial teams highlight stories and write syntheses in a similar way to that of wikipedia and wikinews, but with a strong local, non-internet, face-to-face component. Some people view this local, non-internet participation as leading to a leftist point of view, and suggest that the majority of story posters come from that political persuasion. All indymedia collectives are local and autonomous: some have a policy similar to the neutral point of view, others do not. However, most (but not all) local indymedia collectives encourage passion in the style of reporting used, even while encouraging a synthesis of a wide variety of points of views and links (URLs) to different points of views on what happened and on the context. Moreover, Indymedia is a great source of original text, audio, photo and video reports on current events (even though many newswires contain a lot of spam). This is a potential venue of cooperation between the two projects.
Please, let's make this worthwhile 
I wasn't sure about the best place to make this comment, so here's a link to the place I chose. Please read and comment there: http://demo.wikinews.org/wiki/Wikinews%3ADemo_feedback#Please.2C_let.27s_make_this_worthwhile (this link is dead)