Radon is not dangerous, but its decay daughters are. These can be tested for with those little kits they sell at the home improvement stores.
Just leave it out, open to the air in the room, for at least 2 days and send it back to the lab. Radiation levels of 4 pCi/L (picocuries per liter) and above are considered hazardous to health.
For more information:
To learn more about home radon testing, you should read David Edwards's Ask A Pro Q&A, "Are engineered stone (quartz) countertops really green?"
The EPA's A Citizen's Guide to Radon also offers helpful tips on testing your home for radon.