Water is crucial to survival. In the developed world few people give this a second thought: because of its importance it's freely available, clean and safe to drink. But his situation is the result of large-scale investment and significant effort by numerous employees of the water utilities, dependent in most cases not only on the correct functioning of numerous behind-the-scenes processes and supply chains but also, crucially, electricity. If those processes fail then the water stops flowing.
Failure of the water supply for any period more than a few days will most likely rapidly render urban areas uninhabitable. Whilst it may be possible for relief efforts to provide emergency drinking water supplies in geographically small areas, bulk supply of water is also important for sanitation: flushing toilets and conveying waste through sewers. When sanitation fails the risk of disease rapidly follows.   . It's unreasonable to assume that anything approaching normal sanitation will be available if water supplies are significantly disrupted.
It does not require a sharp-onset emergency to cause severe water supply constraint in large built up areas, nor is it only a problem of far-away lands with poor administration. London in the UK, for example, is close to the limit of existing resources  and in 2018 Cape Town narrowly averted running dry . These are examples of slowly-developing emergencies which can at least be planned for, but should a more pressing situation develop on anything more than the smallest of scale, there seems little doubt that even fully-resourced national effort will be unable to deliver anything close to a 'normal' situation for inhabitants.
The volume (and hence weight, since water weighs 1kg/litre (8 or 10 lbs a gallon us/uk) makes storage of water a highly challenging problem. Hikers and campers can conceivably carry enough for trips of short duration (3-5 litres per day) but this is much less than is typically used by individuals outside of survival situations: even under 'severe rationing' in 2018, the citizens of Cape Town were permitted 50 litres a day and in normal situations US residents use 375 litres per day 
With warning of an impending emergency it may be possible to stockpile water for a few days of use but further than that is likely to be outside of the options for urban residents. Longer term survival will typically involve relocating to somewhere that has some form of reliable supply in the volumes needed. In essence, it's hard to see any mitigation strategy other than rapidly getting out of the affected area to somewhere better.
Due to the critical importance of water to survival the two most important attributes of a water supply are a) drinking quality and b) reliability. Obvious sources such as streams, ponds and rivers may look attractive but in dry periods reliability may suffer and drinking quality is by no means guaranteed. These 'surface water' supplies are subject to contamination from various sources  and must be expected to contain biologically harmful organisms requiring disinfection.
Greater reliability tends to come from large masses of surface water such as lakes and, as has been traditional for centuries, wells and/or boreholes.
None of these sources is perfect and many can be injurious to health in the short or long term. Wells may contain harmful levels of arsenic and flouride. Surface water supplies are notoriously easily contaminated with various pollutants, especially harmful bacteria or viruses (pathogens). This is one of the reasons why collective supply has been an enormous benefit in developed areas, not only can resources be pooled and invested in the reliability of supplies but also in chemical and bacterial testing for safety.
One of the few clean sources of water is rainfall if it can be cleanly collected. Run off from roofs is used in some rural areas and diverted to large cisterns or reservoirs but roofs are subject to pollution from atmospheric sources, bird droppings and leaf fall in deciduous areas.
Deep wells (if properly constructed and prevented from contamination by surface runoff) receive water that has slowly percolated through ground and rocks for long enough to (typically) eliminate bacterial and virus contamination.
In the absence of a reliable and tested water supply one will have to make do with whatever is available. The cleanest and most reliable supply must be located and harvested, there is likely to be little chance of chemically testing it for mineral pollutants. Fortunately, boiling the water is a highly effective way of eliminating the most common pathogens but other methods also exist as listed by the Center for Disease Control
Solar disinfection is also a viable method if a supply of suitable PET plastic drinking bottles is available and there is a good supply of sunlight. Clear (filtered) water is exposed to bright sunlight in PET bottles, ideally with an aluminium reflector (such as corrugated sheet) beneath the bottles to concentrate the light. The combined effect of solar heating and ultra violet light is highly effective in destroying pathogens in water and has the benefit of not requiring fuel nor producing smoke. The longer the exposure to sunlight the better the disinfection.
The matters raised above should make it clear that any emergency which disrupts water supplies across a large area for more than a very short time is likely to be extremely severe. There are no obvious mitigation strategies other than relocating to somewhere that does not have the problem. Creating such a location from scratch requires significant investment (digging or boring a well or installing filtration) unless there is a large natural body of fresh water to hand, since most surface water supplies are unreliable and must be also be presumed to be infected.
This should give long and serious pause for thought to anyone considering a long-term strategy for emergency survival.