How can risk be characterised?

The characterisation of risk has both quantitative and qualitative components to it. These will be described separately.
It should be clear from the above that the type of a hazard and the adverse outcome associated with it is an important qualitative feature of "risk". Thus a specified probability of developing eczema/dermatitis (an inflammation of the skin) would be considered a lesser 'risk' than an identical probability of developing melanoma ( a particularly nasty cancer of the skin).
However, one needs to look more closely to be able to characterise "risk", as distinct from simply `hazard'.
It is clear that the degree of exposure is a very important determinant of risk. Thus as exemplified above, a low exposure to something that is highly hazardous, may result in a low risk. Conversely a high exposure to something of incredibly low hazard may result in a moderate or even high risk therefore every reasonable attempt must be made to attempt quantify and exposure (e.g. to noise, to a specified dust or to radiation) in order to then proceed to attribute a measure at risk to it.
The probability of an adverse outcome i.e. the likelihood of a certain risk can be expressed in various ways. This aspect is so important that it deserves its own section further down.
One must not forget that often statements about causation are made which depend on certain assumptions. Clearly when an assumption about causation is wrong then any associated measure of risk, however accurate numerically, may still even misleading information if it implies that the likelihood of a certain unwanted outcome e.g. cancer, asthma, is specifically and undoubtedly caused by the stated exposure to a defined hazard e.g. particulate chemical dust or vapour.
Therefore statements about risk must also be guided by indication of the uncertainty that may be associated with them. You may wish to find out more about critical appraisal of published literature, for example.
One may wish to know what steps have contributed to a particular risk being so high and/or what steps can be taken to reduce the risk, for example to control the risks from occupational exposures. The cost of these risk reduction measures and their benefits also need to be considered.
Last and not least risk can be perceived by people in different ways. This too is such an important subject that it deserves a section of its own, hereunder.
Risk and the quantification of probability. 
The following account is intentionally simplified. In order to achieve this, "a few corners have been cut". Let us consider the risk to a man dying of lung cancer in any one year, and relate it to moderate and heavy smoking.
Let us assume the following statistics based on a 100,000 men in any one year .......

  If all of these men were non-smokers, one could assume that say 10 of them would die of lung cancer. If all of these men were moderate smokers, let us assume that 100 of them would die of lung cancer in that one year If all of them were heavy smokers let us assume that 200 of them would die of lung cancer in any one year. The absolute risk of dying of lung cancer in moderate smokers would be of 100 men per 100,000 men per year. However 10 men per 100,000 per year would have died even if they hadn't smoked. Therefore the attributable risk in relation to moderate smoking is 90 per 100,000 men per year. Risk could also be expressed in a relative way. In this example the relative risk of dying of lung cancer for moderate smoking (when compared to no smoking at all) would be 100 divided by 10 equals 10 (viz. simply stating that a moderate smoker had a 10 times higher risk of dying of lung cancer in any one year than a non-smoker.

Could you now calculate the attributable risk of lung cancer debts for heavy smoking, and the relative risk for heavy smoking?
Why these different measurements of risk? Some study designs such as case control studies can only provide a measure of relative risk. On the other hand they have the advantage of being cheaper than cohort studies, which give measures of absolute risk.
Consideration of relative risk on its own can be misleading. For example, for the sake of argument, if we said that the relative risk of coronary heart disease in tobacco smokers was two while the relative risk of bladder cancer in tobacco smokers was four what might this imply? It would mean that if you smoked you had twice as high a risk as getting coronary heart disease than if you did not smoke and four times as high a risk of getting bladder cancer than if you did not smoke. It might be misinterpreted to imply that if you smoked your risk of bladder cancer was greater than your risk of coronary heart disease.
From a public health stand point some people might jump to the conclusion that smoking contributes to a greater burden of bladder cancer than it does for coronary heart disease. Of course both these interpretations - as regards the individual or as regards the state of the public health are false. The reason for this is quite simple, the absolute risk of coronary heart disease is much much higher than the absolute risk of bladder cancer. In other words it is much more likely for people to die of heart attacks than to die of bladder cancer if they are non-smokers, and the same is true even if they are smokers.
Risk Factors
There are several classifications, types and definitions of risk factors. One simple approach (although it might ignore many of the terms and definitions found in text books) is the following:
There are those risk factors which were either inherited (genetically) or acquired, but in any case which came before particular exposure to the hazard in question. For example, people who are atopic, i.e. the sort of persons who may have suffered for eczema, dermatitis in childhood, hayfever and asthma may be considered as having a high risk factor, namely their atop, when it comes to considering the likelihood of developing asthma from exposure to say, animals, later on in life.
Smokers may also be at a higher risk of developing say, asbestos related cancer, or some forms of occupational asthma. However whether this is the case because of smoking as antecedent to the later exposure, or concomitant with it is a mood point.
Secondly there are risk factors which are causally related to the likelihood of the adverse health affect. Tobacco has already been mentioned as one possible example.
There are others. Exposure to various agents in the workplace may be causally related to adverse health affects, and therefore these exposures may be deemed as being risk factors causally related to the health effect.
However some risk factors are possibly only surrogates. It may be that residents in a particular city or part of a city is associated with an increased likelihood of say cancer of the bowel. This does not necessarily mean that residents there of itself is a causal factor. It may be that people living in a particular neighbourhood are more likely, for social economic or culture reasons consume a diet that was relatively high in fats and low in fibre.
Perception of Risk
Clearly there are differences in how risks are perceived by scientists such as epidemiologists and others on the one hand and by the lay public on the other hand. Several factors can influence this differential interpretation. These may include:

• Personal experience of the adverse effect/event. 
 
• Social cultural background and beliefs 
 
• The ability to exercise control over a particular risk 

• The extent to which information is gained from different sources e.g. from the media and so on. 

• There are other considerations - for example has been shown that people have a tendency to over estimate very low risk and sometimes to under estimate very high ones.

Tolerability and Acceptability of Risk and what to do about it
Although the scientific community has a very important role to play in measuring risks and in presenting this information in as clear a manner as possible, with appropriate cautions about uncertainty. It is then a responsibility of society as a whole with no particular group having a more privileged position by right, to determine what is tolerable and acceptable based on social, political, cultural and even economic considerations. Clearly there are areas where the risk is so high as to be manifestly unacceptable and others where it is so low as to be negligible. Of course most of the debate is in the grey area in between.
Legislation and attitude and hence behavioural change are important channels for reducing the risk. Many hazards cannot be abolished in the sense that they are completely gotten rid of. Therefore to reduce risk more often than not is a question of reducing exposure. For example in the UK the logic for reducing occupational risks to health is to achieve a situation whereby "exposure should be controlled to a level to which nearly all the population could be exposed day after day, without adverse affects of health".

If you wish, you may find out more about general environmental hazards, or occupational hazards to health in general descriptive terms.