Our most recent and best-documented example of a true siege of this nature is the Siege of Leningrad, where the Germans surrounded Leningrad and cut off all of its supplies for almost 900 days.

What was life like? It was bad. In this siege, the Red Army conscripted any civilian who could lift a shovel to fortify the city, building trenches, building fences and barriers, and so on. In Leningrad, food supply was so low that civilians were rationed 600 grams of bread a day if you worked (imagine trying to do manual labor all day on just 1500 calories!), and far less for non-workers like elderly and children. As the siege wore on, rations were increasingly reserved for military defenders and millions of civilians were subsisting on anywhere from half a slice of bread made of flour and sawdust to literally nothing. Many others froze to death. Reports of cannibalism were widespread. Remember - this was a city of over 3 million! That's a lot of mouths to feed.

Of course, in modern warfare there are also air raids and artillery bombing to deal with. While most Soviet civilians died of starvation, many more died of shelling. When Lake Ladoga freezed over each winter, the Soviets would attempt evacuations of the civilians, many of which failed. The Germans would bomb the lake, set up defensive positions and shoot them as they came, and other atrocities.

Its a tough spot to be in - stay in the city and starve to death, or risk it all to travel across a frozen lake and maybe die anyway.