Students learn in introductory economic that Y = C+I+G +(X-m), which means that GDP is equal to the sum of consumption, investment, government spending and net exports. Those who remember their intro econ are not surprised to see that Italy has slid back into recession for the third time since the 2008 crisis.
Unfortunately simple economic logic does not find its way into the NYT article on the weakness of Italy's economy and much of the rest of the euro zone. The basic story is straightforward. Since 2010 the European Union has been demanding that countries in the euro zone reduce their budget deficits. This means cutting government spending and/or raising taxes. Lower government spending directly reduces demand in the economy. Raising taxes indirectly reduces demand by reducing disposable income, and thereby reducing consumption. (There is a supply-side effect from the change in incentives, but this is in almost all cases much smaller.)
In short, the European Union has been requiring that many of the countries in the Euro zone reduce demand in their economy. There is no obvious mechanism to replace this lost demand. If Italy, Spain, and other countries flirting with recessions had freely floating exchange rates it would be possible that the decline in the value of their currencies would lead to an increase in net exports (a lower valued currency would make their exports cheaper and imports more expensive), but since they are in the euro zone this route is not possible, except insofar as the euro falls against other currencies.
The high unemployment caused by the European Union's polices can have a modest stimulatory effect insofar as they push down wages in these countries. This can improve their competitive position relative to Germany and other countries with stronger economies, but this process is likely to be very slow, especially with inflation running at a very low rate in Germany.
In short, there is no plausible story whereby the countries of southern Europe can expect to replace the demand lost from the deficit reduction demanded by the European Union. The article should have at some point mentioned that the recession in Italy is pretty much exactly what most economists would expect from the European Union's austerity policies, just as physicists expect that when we drop a hammer it falls.