There is a wide range of misconceptions about what is safe and what is not. The matter is sufficiently complicated that a person should have professional advice. However, if there was no doctor going to be available to set a broken leg I presume you would go ahead and do the best you could. And if one had to build a bridge to get across a river and there was no structural engineer around, again I presume one would have a go at it.
Doctor's would like to have their x-ray machines available when setting a leg, and engineers would like to have their surveying equipment, specification guides, and computers or slide rules when they are building a bridge. So you can well imagine a radiological defense officer would like to have radiation detection equipment available when giving advice in a radiation defense situation.
However, if the advise, expertise, or equipment, is not available, one must go on. One rule of thumb is that if there is not enough fallout that you can see it, then there is not enough of it that it will kill you. Fallout is usually small grain dust or grit, often having a light color, but not always. It depends upon its source. The best place to spot it is on a smooth surface, like the hood of a car.
The more dense fallout is, probably the greater the hazard, although there isn't necessarily a direct correlation. It may fall thick enough that quite a little heap of it may be brushed up from a surface that is one foot square. It is possible to build, from common materials found around the home, an expedient radiation detection meter. The details for such a meter are found in books listed in the bibliography.
Even if one has commercially available radiation detection equipment there is still some considerable skill required in its use. For example, almost all survey equipment is designed to be used by an adult of normal stature. This means that if the equipment is held in the hand of a walking adult it will tell how much radiation is being received 3 1/2 feet above the ground, and particularly by the adults vital organs which are above that level. A child's or an infant's vital organs will be below that level and will be exposed to much more hazardous levels than an adult's. For this reason, if one is passing through an area that is suspected to have any radiation at all, a child should be carried on an adult's shoulders.
There is another rule of thumb that for every seven fold increase in time radioactivity will decrease by ten fold. This is called the seven/ten rule. This is based upon standard decay. It is useful as an example, for training, and in building theoretical models, but in actual practice the decay rate is likely to be something quite different. It is determined by the isotopic composition of the matter under consideration.
There is another commonly held misconception among semi-trained individuals that low levels of radiation cannot be rapidly fatal. Someone, after several days in the confines of a cramped expedient shelter, might conclude that because their meters now indicate a very low level of radioactivity (or perhaps no radioactivity if it is a high-range instrument), that it would now be all right to go outside and sleep on the ground in the cool breezes beneath the bright summer stars.
The fallacy again arises from taking measurements at a level that assumes the vital organs are well above the radiation source. This is not the case when a person is stretched out on the ground for long hours of sleep. These long hours of low level radiation exposure to the vital organs will result in a fatality in just a few days.
Likewise, perfectly healthy adults who take infants out of the cramped, unpleasant, expedient shelter to allow them to play during the day on a blanket spread out on the ground will be quite shocked to see those infants sicken and die in just a few days while they themselves remain healthy. The infant's vital organs again being close to the weak radiation source for a long period while the adults' vital organs are being protected by distance.