food/shield/trade of city tile

Does anyone know how this works exactly?

I think this is explained in detail in DaveV's guide to ICS, which you can find a link to in the GOTM Rules thread, which is here:

http://forums.civfanatics.com/showthread.php?p=8890112#post8890112

(see post #270). Or, if you have a specific question, probably someone here can answer.

Basically, it is the same food/shield/trade output you get from a none-city-tile. However, in a city you automatically have irrigation and roads (and bridges if you found your city on a river tile, if you have not discovered bridge-building). Irrigation turns to farmland and road turns to railroad automatically once you discover refrigeration/railroad. One exception is mountains, a mountain city generates one food, whereas a none-city mountain tile worked on does not.
And there is this issue with mining: You cannot build a mine in city on hills/mountains (you can cut down trees in a forest-city though) and if you build a city on an existing mine on hills/mountains, that mine is destroyed by the automated irrigation. The trick to have a hill-city with a mine is to let one settler/engineer start to build that mine and found the city with another. That way, you have the automated irrigation, but the settler/engineer keeps on mining, eventually destroying the irrigation with the completion of the mine.

Major Advantage said:

One exception is mountains, a mountain city generates one food, whereas a none-city mountain tile worked on does not.

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The other exception is that if the city center does not already produce a shield, one will be produced. Thus building on non-shield grassland, jungle, swamp, ... you will get a shield that is otherwise not there.

Major Advantage said:

And there is this issue with mining: You cannot build a mine in city on hills/mountains (you can cut down trees in a forest-city though) and if you build a city on an existing mine on hills/mountains, that mine is destroyed by the automated irrigation. The trick to have a hill-city with a mine is to let one settler/engineer start to build that mine and found the city with another. That way, you have the automated irrigation, but the settler/engineer keeps on mining, eventually destroying the irrigation with the completion of the mine.

Click to expand...

The irrigation does not get destroyed. Once the worker is done, you get the benefits of both irrigation and mining. This and the added defense makes hilltop cities worthwhile despite the lack of arrows at the city center.