A lot of new houses built now just use a thick plastic sheet/tarpaulin as Radon protection. That works, but if you don't have it, keeping any enclosed spaces aired or using an extractor fan is plenty.
As a source - Radon comes from the bedrock. So, more of a problem in cellars and basements than anything else.
Given the size and behaviour or Radon ions, they cannot pass through thick plastic, a decent amount of concrete, or anything with a bit of thickness. The daughter isotopes (Lead, mostly) are immobile, so once it decays (below a membrane/barrier) you don't have to worry about it. The way it decays also (Beta radiation, if I remember correctly) means it's decay radiation is also stopped by plastic or concrete.
Seal any cracks or possible entryways for the gas, air out the place, and that alone will probably reduce the levels. Plastic sheeting will be a bugger to fit, but then, so will every other mitigation method.
(Most of that is stuff remembered from uni (Geology degree), and from living in a couple of houses over a Radon hotspot. A rock by the name of Northamptonshire Ironstone, which is high in Potassium, which tends to adsorb Radon and it's parent isotopes particularly well...)