Scrape off the top layer, grow the right kind of crops

Fallout is essentially dust. It is not something that infuses everything and cannot be gotten rid of. You need to remove the top layer of soil a — and with that the contamination — and from then on the ground is fine to use.

Also it helps if you grow the right kind of crops. In some the contamination will be spread evenly through the edible parts, in others — such as stone fruits— the contamination tends to be concentrated to the seed while the flesh is all fine.

Much information about this can found from the Chernobyl Recovery and Rehabilitation Programme

As far as water is concerned, the constant runoff and replenishment will quickly dilute the contamination in water. Especially streams and rivers of fresh water will be a safe source to use for drinking and irrigation.

Also, as was concluded in other answers: there is a huge difference between peacetime concerns for radiation and a situation like that which you are describing. You can easily increase your yearly dose of radiation to 250 - 500 mSv, which is an increase of about 10 000% compared to present day conditions, without any acute ill effects, only increasing your probability of some cancers by a few percent.