I have been building Pioneers to make other cities and getting caravans between them. But I don't know if that helps since I got my third city up last night before going to bed. But when I see a special resource I build a city next to it, if it is away from another city.
If you click on a caravan once their route is established, you can see the food bonus theyre currently providing.
There's more tech available to boost food production than almost any other resource it seems, so do don't neglect your civics research.
Don't establish cities willy nilly. Have a good reason for doing so, A single resource tile is probably not a good enough reason to found a city, unless it is a vital resource that you have to have right then. There should be several attractive resource tiles in the eventual influence of a new city, or it's probably not worth the tradeoffs from founding a new city.