The system takes some getting used to, but it's actually very elegant and simple once it 'clicks' for you. Here are a few tips:
- Cities that have plenty of food probably have their stockpile level set to 75% or 100% -- turn them down to 50% or even 25%, so they'll ship more food out. (Use the up/down arrow buttons on the city info panel.)
- Cities that are on the frontier where you expect to campaign and have a lot of troops, turn their stockpile level up to 75% or 100% so they'll request food from the cities that are shipping it out.
- Upgrade trade routes from your food-rich areas to the food-starved areas so they can transport more food per week, thus keeping up with the increased needs of those frontier cities. (Click on the route, then the up arrow to upgrade it -- note this will cost more money with each upgrade, which is one reason you always want to try and keep a little extra gold income as a backup at all times.) If you get a rebellion caused by a starving city, you can often quell it just by upgrading a trade route to a city with a food surplus.
You need to go carefully over your cities and routes -- the parchment map is great because it will show you where food is piling up, and where it's needed. Spend a few minutes sorting the logistics network out, and also make sure all your farms are connected (it's easy to miss a few in the hectic pace of this game).
Finally... SHEEP! Sheep are worth their weight in gold. Collect them whenever they appear, and send them towards cities that are having food trouble. A flock in the right place at the right time (i.e. late winter or early spring) can mean the difference between a rebellion or a fat, happy city...