Sieges in World War 2 came down to how well they could manage supply lines into the city. In Stalingrad for example the Air Supply line was woefully inadequate for the German's 6th Army but in the example of Leningrad there is little doubt the well managed supply infrastructure via lake Ladoga saved the city.
Leningrad is probably the most famous and most brutal example of a city under siege during the war. Army Group North of Germany and the Finnish Defence forces were able to cut the city off from the south and north respectively in late 1941. Once the city was encircled the Germans stopped at the city for fear of being responsible for feeding and caring for the population during the winter, this was consistent with the Hunger Plan that sought to bring down the number of Eastern Slavs to a more manageable number - also a pragmatic consideration given German supply problems at the time. Despite the encirclement, Soviet forces were later able to bring supplies in over the frozen Lake Ladoga which became known as the 'Ice Road' or 'Road of Life', they secured the supply line with flak emplacements and snow huts on the ice. Eventually the Russians would perfect this supply line, building Oil and phone lines in it, the road was used until 1943 when the Russians were able to construct a railway to the city via a small corridor the Red Army was able to open up to the city.
Life in Lenningrad was very difficult, food stores were nowhere near enough and rationing was introduced. Dead relatives would be hidden away so they could use their ration card and slowly pets began to dissappear. Eventually people would even resort to cannibalism though most of those consumed were already dead, rumours circulated that young women made for the best meat. Cannibalism where a person was killed for the purpose of being eaten was apparently rare though. German artillery and bombing was also a constant issue for the city.
If you were one of the lucky ones to get evacuated from the city you still ran the risk of getting killed on the Ice Road either through being too weak from the hunger, traveling vast distances in the height of Winter or from Luftwaffe or Artillery strikes. Over 1.2 Million civilians were evacuated via the Ice Road.
Leningrad would eventually serve as an example for Hitlers 'Fortress Cities' but with very different results. Despite the fact Air Supply had proved inadequate at Stalingrad - though the theory had worked earlier in supplying the Demyansk Pocket - Hitler continued to order forces to hold their ground and supply them by Air or Sea. This would have disastrous results in the Siege of Budapest where encircled Hungarian and Germany Armys would be refused permission to breakout and would slowly lose ground in the city to he soviets, eventually attempting a breakout too late to be successful. Goebbels built plans around holding Berlin as a fortress city with Leningrad as a model, having radios in every apartment building and fighting block for block, but without a supply line and being encircled on all sides of the landlocked city this would've been unfeasible, as Colonel Rudel pointed out to the propaganda minister, though Goebbels wouldn't listen.