Basically, connect cities to nearby farms and there will be a steady stream of food from farm to city... with seasonal variation: very little in winter, max during the fall harvest. There is no food available while a farm is burning and none transfered while it is cut off.

For historical and gameplay reasons, some cities have an abundance of food while others have very little forcing them to rely more on flocks of sheep.

When a city has excess food it pushes it toward cities that have less. The longer the supply line the slower the transfer rate. Merchant shipping routes move about 10x more food than land routes and are less effected by distance.

You can set a city to hoard more food to help stockpile for campaigns,etc.

You can also load up workers to manually move food quickly to a city in need.

Protect your supply lines or make sure there is enough food around to survive disruptions.

-Jim

Cities that have less food than their target will automatically request a food transfer from other cities and forts they are connected to. If these cities are also low on food they will reject the request but if they have met their target or have extra food they will start transferring food and will pass along the request to additional cities that they are connected to.

So to answer your question, food will move automatically from one side of your kingdom to the other as long as each city on the route has met or exceeded their own targets.

I hope this answers your questions. As you've noticed from some of the other discussions, I've been considering adding a few more options to control this: namely a 'max' target that will let a city continue to receive food indefinitely as well as adjusting the priorities so that a city will still hand out food to nearby units even when it's below it's cap as long as it has some basic minimum.