Of course we have a bit of a problem in that many of the people you will be arguing against will not consider your source to be reputable. Even user-edited and well referenced sites like Wikipedia are thought to be suspicious. Snopes is questionable, and even the more "mainstream" conspiracy sites like Above Top Secret are not above suspicion.
There's no magic right way of doing this that's going to immediately convince everyone. This is a game of inches.
So what are my go-to web sites?
First of all, check if there something that pops up at the top of the google results. Search for "subject debunked", (e.g. 9/11 debunked) and you get www.debunking911.com and http://www.popularmechanics.com/tech...y/news/1227842, which is pretty much all you need for a general debunking. You can extend this to a particular topic, like "no building collapsed due to fire 9/11 debunked", which takes you to the appropriate page: http://www.debunking911.com/firsttime.htm. You can also use google to limit your search to one of the sites below, like site:contrailscience.com
Google will also pop up links to a number of the following sites, and you'll probably arrive at the site's material via Google more often than going directly. But the following list still gives you a good idea of what google links to click on first.
Wikipedia
Wikipedia is a great resource, usually giving a fairly detailed exposition of the theory, but also because of its insistence on all claims being backed up with citations, it gives you a lot of very well backed evidence. One area where it fails somewhat is that it does not consider blogs to be reputable sources, so often excludes them from a page, despite how interesting or relevant they might be. So for more niche topics, the most comprehensive debunking treatments might not be linked from the Wikipedia article.
Snopes
Snopes is pretty light weight, but it covers a lot of topics. The focus is more on urban legends, and chain letters, so most of the articles there are just about debunking stories that your aunt might forward to everyone on her email list. But they do include some quite detailed debunkings of various things that are floating out there in conjunction with a larger conspiracy theory. Such as a supposed photo of Obama's Kenyan birth certificate.. Here several sources are given, but not linked.
Archive.org
Google will often give you a page that contains useful links to other pages that are now dead. This is particularly true for individual web sites and blogs set up to debunk a story anything over a few years ago. This site http://goodsky.homestead.com/files/linesinsky.html has a link to a story back from the pre-history of the chemtrail hoax. http://www.sightings.com/health/antvacccures.htm but if we try it in archive.org http://web.archive.org/web/*/http://...tvacccures.htm , we get the full history of the page dating back to 1999. http://web.archive.org/web/*/http://...tvacccures.htm
If a web site no longer exists, then it's pretty safe to link to the archived version. However if a web site is still active, and they removed the material to hide it, then you want to make a local copy of the material, and preferably post (or fingerprint) it publicly as soon as possible. A web site owner can get all its prior material pulled from archive.org. So keep that in mind. In general, you should ALWAYS keep a local copy of anything that you cite, just in case it vanishes from the web. Copyright law allows you to make reasonable copies of material for individual personal use. You can also quote sections of material under the fair use provisions.
The Skeptic's Dictionary
http://www.skepdic.com/
A very comprehensive list of skeptical topics and the nomenclature associated with them. Individual entries have a quick overview, and then usually several useful links.
Debunkatron
http://debunkatron.com/
An excellent list of bunk-like subjects, together with up-to-date links that provide the best debunking explanations of them.
Above Top Secret, etc.


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