Keeping a healthy food supply is not easy in this game. You have to balance production between food and other resources well or you will crumble.
1. Managing early
Early on you need cows. Set every field to cows in the very start, with no grain. Dairy produces 5 food for existing. It is, at least early, more effective than grain.
2. The middle stages of the game.
After you have 150 or so cows (and near 1,000 population) you need some grain. Buy some from the merchant and plant 2 or so fields. Each field requires 20 grain to plant.
Move the food allocation ALL THE WAY to the grain side. You don't want your people eating your cows. If you start losing cows, then sell them or move them. If they die you get nothing out of them. Its better for them to reproduce :)
3. Later in the game
Later you do not need Cows as much. You can survive on grain only. However, it is nice to have a few cows, because of the free food they give. :) Grain is rather reliable, but because it can only be harvested once a season, its nice to have a few cows.
Grain does produce a LOT of food. Each square produces 240 units of grain in the fall for 20 harvested in the previous winter. You need to play around with a method for food. Generally, if a county has fewer squares, you should try and put grain because it will produce more in the long run.
4. Army foraging, Advanced Farming
Army foraging
This makes your life more difficult. You now cannot simply raise an army when the pop. growth gets greater. As the population goes up above 1000, raise an army, for sure, but also decrease rations and raise taxes. Also, try to keep your armies in unconquered colonies and enemy colonies. This drains your enemy's food supply. Also you HAVE to use all your troops quickly. Either put them in a castle (They don't forage in a castle) or move them away. Just keep them away from your counties.
Advanced farming
This makes the crops dependant on fertility and weather. Leave 1/3 or so of your fields open and you'll get a strong yield.