Building codes where I am, outside of Chicago, have required all new homes to have passive radon venting installed during construction for at least twenty years. This is a length of PVC pipe that runs from just inside the sump pit in the basement (lowest point) all the way through the house and up out the roof. The sump pit also has a sealed plastic cover bolted on.

It's then elementary to buy a radon fan and install it in that PVC pipe in the attic, making it an active system. You want to have less than 4pCi/l (picocuries per liter) radiation. My basement office used to be like 23pCi/l. After installing a fan (and then later replacing it when the first one stopped doing its job), it's at 1.6pCi/l.

Most of the radon tests out there are "single use," where you set the test down, wait for some period of time, send it off to be analyzed. These are like US$20 or US$30. One company makes a plug-in detector that runs all the time, and alarms when it's over 4pCi/l. It's about US$130, and worth every penny if you have a finished basement and anyone spends time in it.

Edit: A quick look at Amazon shows that the garbage companies are now making always on radon detectors. This is new since I bought mine like five or six years ago. You want a SafetySiren brand, and the newest model is now US$180 on Amazon.