A tile have to be of a certain grain/material value (6 I think) before you can settle/see the tile yields of the specific tile
A tile have to NOT be within 6 (I think) tiles of another city.
Grass in general boosts grain of nearby tiles,
Forests in general boosts material of nearby tiles,
Rivers in general boosts grain of nearby tiles,
Shards in general boosts the essence of nearby tiles,
other resources usually boost in certain way, clay pits adds a little material I think, for example.
You only use the tile yields of the tile you settle, because it is the sum yields of the surroundings.
If a city was constructed on a location, and then razed, the area around where the city was located will be without grain, and therefore without yields.
Sincerely
~ Kongdej