Radon (more specifically Radon-222) is produced in the decay chain of Uranium-238. Radon-223 is also produced by the decay chain of Uranium-235 and Radon-220 is produced by the decay chain of Thorium-232 but both Radon-223 and Radon-220 have half-lives of less than a minute, so they almost never reach the atmosphere where they can be breathed in because they mostly form underground and they decay too quickly to reach the atmosphere.
Radon is unusual in that it's the only noble gas along the 4 primary decay chains and only the Uranium to Lead chain produces Radon-222 which has half life long enough to reach the atmosphere and get breathed in.
More on decay chains here and here.
Uranium-238 has half life of about 4.5 billion years, so about half the Uranium-238 that was present when the Earth formed is still here. It decays very slowly, which is why it's not dangerous to be around Uranium in it's natural form. (though if somebody hands you a block of it, you might still want to wash your hands after touching it - then call national security) . . . but I digress.
Radon-222 has a very short half life of 3.8 days, so while the Uranium that produces it decays very slowly, the Radon is highly radioactive and it decays (into other radioactive elements) quite rapidly. If you had a sample of Radon-222 for example, in less than a month, 99% of your sample would be gone.
Because it forms slowly and decays quickly it never collects beyond a very trace concentration and it continuously needs to be regenerated.
Houses with a Radon problem need to be continuously ventilated because of that regeneration. At least/about two or three times a day I would think (see comment directly below, once a day may be sufficient), but it's worth pointing out that the Radon in houses is so faint that it takes months, if not years, for any kind of health problems to arise. It's kind of a weird thing. It's not dangerous at all to walk through a house with unsafe Radon levels, similar to how it's not dangerous to visit Chernobyl. It's just not a good idea to live there.
Radon is also likely to only be a problem in poorly ventilated houses, (basement's especially, because the heavy gas tends to settle) but a good ventilation system should make any house safe. And it's more common in specific areas.
There's the problem of keeping the house warm in winter and maintaining ventilation, because ventilation does need to be maintained. Houses can be also built above ground to reduce exposure.
As a general rule, it's the ingestion, either breathing or swallowing of radioactive material that's most dangerous. That's why it's a good idea to put on a gas mask to prevent breathing in any radioactive dust or fallout (though a gas mask won't keep gas like Radon out). And it's a good idea to leave your clothes in a separate changing room and shower thoroughly if exposed or walking through radioactive fallout - that has nothing to do with your question, just putting it out there. Also the opposite applies if there's radiation outside from a nuclear accident or bomb- close all windows and try to keep ventilation as close to zero as possible, at least for a day or so until you get instruction on the levels, but . . . I digress. Point is, because Radon is easily breathed in, it's quite toxic even in very small amounts. At the same time, the Radon concentration inside houses with a radon problem is so small, that it still takes months if not years of exposure to lead to problems.
That's why Geiger-counters aren't used to test for Radon. There's too little radiation. You need specific Radon detectors.
Are these rocks common?
Yes, and no. Because the gas comes from Uranium, (and mostly from underground), Uranium isn't exactly common but it's not super-rare either.
How do these rock’s become radioactively charged?
This was covered above, but Uranium, in small amounts, is in lots of different places. The Rocks were always (mildly) radioactive.
Pictures or examples?
To my knowledge, pictures or examples don't do any good because trace amounts of Uranium in rocks doesn't look any different. Besides, most of the Uranium is underground. You have to rely on Radon testing and look at locations where Radon is more of a problem. If you live and work above the first floor, and not near a mine or massive dig-site, you probably have little to worry about. If you live in a basement, you should have it checked out.
On the process
The Uranium or U-238 goes through several steps in it's decay and this chain is only the most common outcome. Part of the problem with Radon, is if you breath it in, and don't breath it out, it becomes Polonium and goes through a few other steps. In high enough concentration, Radon is extremely toxic. From rocks, the concentration that's likely to form in a house is usually low enough that harmful exposure takes months or years.