For neutral or enemy cities, the City window will display the owner of the city if you can "see" the city (i. e. have a unit in its neighbourhood). For your own cities, you can use this window to choose the unit type that is produced.
If a unit is produced in the city, the unit type is selected in the listbox. A black bar shows the progress of the production; but you can't exactly see how many more turns it will take to finish the unit.
In order to change the unit type that is built, just choose another unit type and select the "Change" button.
You can open the city window by clicking the right mouse button on the desired city. You can leave the city window open during your turn. Whenever you do a right mouse button click on another city, the window will be filled with the information about that city. You can close the window by choosing the OK button.
Never close the city window directly using your window manager!