There's so much to this game, it's easy to overlook little things like the need for sewer systems to get over size 12. You've come to the right place for help, here you get more than you asked for!
Your cities try to grow when their food box is full at the beginning of your turn. If the city is at least size 8 and doesn't have an aqueduct, or size 12 and doesn't have both aqueduct and sewer system, it won't succeed in growing, but it will empty the city's food box and you just lose all that food.
Granaries are less complicated than they seem. When your city tries to grow, a granary saves half the food in your food box; a 50% head start toward growing again. It's a very helpful boost for new cities, but there are problems. Granaries are very expensive to build, whether you're spending gold or shields, and they cost 1 gold per turn to maintain. That's not such a high price but it's usually all a small city produces. You're almost always better off building the Pyramids, which cost as much as 4 granaries and give the same effect to all your cities, with no upkeep at all.
And the bonus advanced tip: aqueducts, sewer systems, and granaries don't help you at all if your cities aren't growing. You need some of these improvements to reach that size, but once you get there, you can sell them. No more maintenance cost, and a quick bit of cash to buy more caravans.
