We have had our home tested and done radon remediation. The test is really not that expensive. I would suggest first buying the short term test (like 3 days, I think) to give you an idea of whether there might be a problem. They are about $10 to get yourself and you send them off to a lab and they report the results online.
If the result is over 3 (picocuries per liter) or so, you should probably do a longer-term test because radon levels can fluctuate significantly depending on weather, seasons etc. Those tests take between 1 month and a year (the longer you leave it, the more accurate) and cost about $25 or so, I think.
For example, when we bought our house the short term test came up at 4.2, just over the EPA recommended limit. We did a long-term test for 3 months and the level was over 9! So we did the remediation, which cost $1000, and now we have a little fan that sucks the radon from the ground beneath our house and vents it above the roofline.
You might get an idea of whether radon is a problem in your neighbourhood by asking neighbours who've bought their homes in the last few years whether they had a test. The contractor we hired for remediation had done about 5 houses on our street. We knew that our town has high radon levels, so we were looking out for it all along.