What is your understanding of Occam's razor, and how exactly does it unequivocally negate all conspiracy theories?

I try reading about Occam’s Razor and my head starts spinning, so while I will continue to try to understand it, I am throwing this out to the collective. I’m also tired of people’s tendency to call “Occam’s Razor!” as if that definitively ends the discussion. Please show your work.

A couple of resources that are used to compile the Wikipedia entry:

http://skepdic.com/occam.html
http://www.physics.adelaide.edu.au/~dkoks/Faq/General/occam.html
http://www.theness.com/articles.asp?id=71 (you’ll notice this one also negates wild theories but doesn’t say how)
http://people.howstuffworks.com/occams-razor.htm (to me this is the best illustration of my question, plus the video on this page does a really good job of illustrating how it can cut both ways and still not answer the question)

Of note:

Occam’s razor is often cited in stronger forms than Occam intended, as in the following statements. . .

“If you have two theories that both explain the observed facts, then you should use the simplest until more evidence comes along”

“The simplest explanation for some phenomenon is more likely to be accurate than more complicated explanations.”

“If you have two equally likely solutions to a problem, choose the simplest.”

“The explanation requiring the fewest assumptions is most likely to be correct.”

. . .or in the only form that takes its own advice. . .
“Keep things simple!”

and

Skeptics use Occam’s razor as a fundamental tool and sometimes as evidence itself. Skeptics are people who tend to believe only what they can sense or what can be proven scientifically. This makes them foils to people who believe in conspiracy theories and religious beliefs.

But a true skeptic will tell you that he only uses Occam’s razor as a tool for considering different explanations. Skeptics who truly appreciate the healthy investigation of the universe use Occam’s razor to pick the simplest (and in their belief, most logical) explanation, but stop short of using it to discount other, more complex explanations. After all, evidence could come to light later on that shows the more fantastic is true, and a true skeptic’s aim is to keep an open mind.

There are, however, some—skeptics and scientists alike—who wield the razor like a broadsword. To these people it proves one theory and disproves another. There are two problems with using Occam’s razor as a tool to prove or disprove an explanation. One, determining whether or not something is simple (say, empirical evidence) is subjective—meaning it’s up to the individual to interpret its simplicity. Two, there’s no evidence that supports the notion that simplicity equals truth.