It is worth reading http://webpages.charter.net/dkessler/files/KesSym.html and some of the linked articles in that article are also very informative reading, altough can be quite technical.
The first thing is that a cascade does not happen in a matter of days or even months. Instead what happens is increasing density of debris reduces the expected lifetime of a satellite.
Not all orbits are affected. The main problematic orbit is low earth orbit. Very low orbits, where atmospheric drag is significant, will not be badly affected because the atmosphere will quickly remove debris. Below around 800 km atmospheric drag will be reasonably effective as the orbits of debris will decay in the matter of decades.
Particularly problematic is low earth orbits in the range 800-2000km, at these altitudes it takes centuries for atmospheric drag to remove debris, the debris in those orbits stay. With nothing removing the debris, the density is free to build up from collisions. The low rate of orbital decay and the fact that they are below the van allen belts are factors which make these altitudes attractive for satellites.
Even in the worst case scenario, the low low earth orbit would remain reasonably hospitable because the atmosphere is quickly removing the debris and the very stability of the higher orbits means the debris flux from higher orbits would be reasonably low. During the worst of a kessler syndrome cascade there would be significant extra debris even at very low earth orbit, but it would improve in a matter of years.
In higher orbits, the orbit doesn't become unusable per se. Instead what you have is probabilities. With a desired mission lifetime in mind, a level of shielding is required for a certain probability of achieving that lifetime. Above a certain projectile mass (~100g) shielding becomes impractical. However, the same debris which are too large to shield against, are also large enough to track effectively, so active collision avoidance could be used. Both shielding and provision for active avoidance adds mass and complexity to the satellite.
Middle Earth Orbits will not be badly affected because the density of satellites is much lower. The density of satellites is much lower because these orbits are not as useful (also the van allen belts are found in MEO, and are problematic for satellites at certain altitudes). A satellite would still need to pass through the LEO debris belt, but it comes back down to probabilities, there is a probability of collision which damages the satellite, and you can add shielding to reduce the probability of damage to a level deemed acceptable. Also, a path can be plotted which avoids trackable debris.
In summary then, even in the case of a very bad kessler syndrome, very low earth orbits, where orbital decay measured on the matter of years, will remain quite usable. Collision avoidance and shielding can be used to reduce probability of satellite destruction to acceptable levels. It may be the case that certain altitude ranges become effectively unusable because the expense of making a satellite which can survive in the debris belt, would be greater than the expense of either having the satellite in a lower orbit (requiring frequent boosting) or a higher orbit (requiring a more powerful rocket and a dangerous pass through the worst of the debris). I think the impact of a kessler syndrome is sometimes exaggerated, although being deprived of the most useful altitudes and the destruction of nearly all existing LEO satellites would certainly be very harmful to humanity's ventures in space.