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This is something I have hard time understanding. Most of the stars are having star flares most of the time. If they're like our Sol, they have periods of high and low flares activity, but within the periods the pattern is random (i.e. noise). Presumably, the change in luminosity caused by a random flare is bigger than by a planet transit (remember transit of Venus?). So how are they filtering the noise out?

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There's no quick answer to that question, unfortunately, because if you want something other than handwaving the answer is to go learn about the basics of signal processing. But in short, the signature of a set of random flares and a regular crossing of a planet are sufficiently different that they are easily separated by the correct tools, the frequencies are totally different.

Are there any resources you could recommend for learning about signal processing?

You could try reading (and working through) "Structure and Interpretation of Signals and Systems".

That's a really good question. From my understanding, solar flares themselves can't be detected optically yet. Note: It may very well be possible that Kepler can do this, but I don't know. I'm just an amateur. In one instance of extrasolar flare detection, http://www.nasa.gov/mission_pages/swift/bursts/monster_flare..., it was found by SWIFT detecting high x-rays coming from II Pegasi. Basically, this is why detecting multiple transits is necessary. Its entirely possible to see some stellar activity that looks like a transit. However, its very unlikely that multiple observations of transits that match each other can be attributed to solar flares.

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