If you've been told about something for the first time (for example ice circles from William Shatner's "Weird or What?"), what resources (eg specific websites) would you use to determine if it's real or not?
Well, if it's something like a treatment or a phenomenon that there is a well defined term for, and you just want to read up on whether or not there's scientific support for it, I'd say Skepdic is a handy resource.
If it's something completely novel; apply skepticism. That's not the same as dismissing something. If you can't determine if something's real or woo, then you can't, and you should approach it accordingly. It's less credible than something that's been proven real, and it's more credible than something that's proved to be woo. This is where you can unleash your own common sense, and just ponder how plausible it sounds.
Sometimes you'll be wrong. Lucky for you, skepticism is not about 'being right all the time'. Looking back at this image of the Guatemala sink hole, I remember thinking it looked pretty damn photoshopped. I still reckon it does!
Back then, this was pretty much the only image you could find, wherever you looked, and everybody was citing the same loose news story. All warning flags up - be skeptic about this one!
The reason I picked that example is that I no longer doubt that it exists. My skepticism led me to the wrong conclusion, but that doesn't mean I was wrong to apply it. So what's with the rant? Well, what I'm trying to say is simply that as long as your default mode is skepticism, you can be reservedly optimistic about a news item or cautiously dubious. Be aware that you don't know, and you'll be fine.
The cases where you can actually go to a source and read up on something are the boring cases. For those, Skepdic or Wikipedia will do.
Reliable go-to sources are not an excuse not to be skeptic, anyway. The Oxford English Dictionary had the wrong definition for how a siphon works for a hundred years, remember.
Your question seems to be more on seeking then on skepticism. The general approach would be: Find something on the internet (using search-engines, but also to batlle 'the hidden web', special database-drive sites), check your source, repeat.
But to give some more substance to this answer:
Meta / General advice
Start out by searching the site your are looking at If you cannot find the answer, but you do find questions, come back and add your findings as an answer after you've searched
Looked down upon as it may be, wikipedia is a great resource. Or better, Meta-resource. If you can find a good article, the references are the stuff you are looking for. The general information on the page should be referenced (if you are lucky), and you should use these references as a starting point. As it is wikipedia, check these references for validity.
Even more meta is ofcourse google: look up your subject, and then do the meta-check: find out something about the formerly-unknown-to-you sources. You can try to pinpoint known sources using the
The various skeptic societies have a lot of articles online. But most of the time they are easily found using google, or even better: the specific pages within their sites (about your subject) can be found like that.
Urban legends: Snopes
Another good startingpoint might be Snopes, for those hard-to-kill urban legends.
The go-to site for medical articles is PubMed
More could be added later, I must be off to work now
For scientific questions, a better resource than Google is Google Scholar. This searches for scientific articles. Caveat: It looks for documents that are formatted like scientific articles. This does not automatically mean that the article has any scientific merit. Look what Journal the article appears in. Is it Nature, or is it the Journal of Homeopathy and Woo?
If you are affiliated with a University, chances are you have access to the ISI Web of Knowledge, which is a powerful database for scientific publications.