It's probably best to point you to the underlying concepts/mechanisms to make sure that you can understand those. I'll be brief --
- the fat cross, the 20 tiles around each city that you see in the city manager
- for each point of population a city either works a tile or runs a specialist
- pop growth is from food surplus, which = (food from tiles worked) - ((pop-1)*2) - (net unhealth)
- if 2 cities have overlapping fat crosses you can choose which city may work each overlapping tile by going into its city manager and clicking the tile
Basically for a beginner my advice is that some overlap is no problem, but it is important to make sure each city has exclusive access to one or two food resources. (Worst case, farmed flood plains -- very worst case, farmed grassland -- but you need to be experienced to judge when that is worth it, so I don't recommend it.)
johnny_rico's thing about sharing food squares is an advanced micromanagement technique involving swapping which city is allowed to work a food tile at different times.