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I'm not a brain in a jar. How can I prove this? I don't have to. It's obvious I'm not a brain in a jar. Or, as Heidegger would put it, I am always already within-the-world. My world is what is real to me in my facticity, or, in other words, the world is what it is for me. So, even if there are other beings who might perceive me as being a brain in a vat, my world is such that I am not a brain in a vat. I'm a student typing at a computer in east Germany.
To more, the (slightly) more interesting question is "How do I know I'm not dreaming?" That also seems easy to me. When I'm dreaming, to the extent I think about, I know I'm dreaming. So it's not hard to know I'm not dreaming, either.
Sorry to be somewhat dismissive. I do like the notion of actually talking about something other than religion on a philosophy board -- doesn't seem to happen too often.
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"Die Deutschen meinen, daß die Kraft sich in Härte und Grausamkeit offenbaren müsse, sie unterwerfen sich dann gerne und mit Bewunderung:[...]. Daß es Kraft giebt in der Milde und Stille, das glauben sie nicht leicht."
"The Germans believe that power must reveal itself in hardness and cruelty and then submit themselves gladly and with admiration[...]. They do not believe readily that there is power in meekness and calm."
-- Friedrich Nietzsche
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